what will be the nature of roots of quadratic equation 2x²+4x-7=0?

Answers

Answer 1
Understanding Concept :-

Let us consider a quadratic equation αx² + βx + c = 0, then nature of roots of quadratic equation depends upon Discriminant (D) of the quadratic equation.

If Discriminant, D > 0, then roots of the equation are real and unequal.

If Discriminant, D = 0, then roots of the equation are real and equal.

If Discriminant, D < 0, then roots of the equation are unreal or complex or imaginary.

Where,

[tex]\quad\red{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]

Given Equation:-

[tex]\red{\leadsto}\: \sf{2x^2 + 4x -7= 0} [/tex]

α = 2β = 4c = -7

Now,

[tex]\quad\green{ \underline { \boxed{ \sf{Discriminant, D = β² - 4αc}}}} [/tex]

[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 4^2-4\times 2\times ( - 7) \end{gathered} \end{gathered} [/tex]

[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 16-( - 56)\end{gathered} \end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf D = 16 + 56\end{gathered}[/tex]

[tex]\begin{gathered}\begin{gathered}\implies\quad \sf D = 72 \end{gathered} \end{gathered} [/tex]

Since, Discriminant, D > 0, then roots of the equation are real and distinct.


Related Questions

24 candy bars cost $48.
How much do 10
candy bars cost?

Answers

Answer: $20

$48/24 = $2 for each candy bar

10 candy bars * $2 = $20

Find the volume of the cylinder. Enter the answer EXACTLY as it appears on
your calculator. NO ROUNDING this time.

Answers

Answer:

653.45

Step-by-step explanation:

How are the two shapes
similar?

Answers

Answer:

they arent

Step-by-step explanation:

maybe height or width

i dunno

- Simplify (3x - 5) + (5x + 1). O 8x - 6 O 8x +4 - O 8x - 4 O 2x - 4​

Answers

Answer:

8x - 4

Step-by-step explanation:

3x - 5 + 5x + 1

8x - 4

the answer is 8x-4 because
3x+-5+5x+1
=(3x+5x)+(-5+1)
=8X+-4

help meh out please:)

Answers

The distance between two points is the number of units between them

The distance between the oak tree and the maple tree is 9 yards

How to determine the distance?

From the diagram, we have the following highlights:

The distance between the maple tree and the end is [tex]28\frac 26[/tex] yardsThe distance between the oak tree and the end is [tex]11\frac 36 + 7\frac 56[/tex] yards

The distance (d) between the oak tree and the maple tree is the difference between the above measurements.

So, we have:

[tex]d = 28\frac 26 - (11\frac 36 + 7\frac 56)[/tex]

Simplify the expression in the bracket

[tex]d = 28\frac 26 - (19\frac 26)[/tex]

Subtract

[tex]d = 9[/tex]

Hence, the distance between the oak tree and the maple tree is 9 yards

Read more about distance at:

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The distance between the maple tree and the oak tree is 9 yards

The distance between the maple tree and the end is 28 2 / 6 yards(170 / 6)

The distance between the oak tree to the end is the sum of  oak to pine and pine to the end. Therefore,

11 3 / 6 + 7 5 / 669 / 6 + 47 / 6 = 69 + 47 / 6 = 116 / 6 = 58 / 3 yards

Therefore, the distance between the maple tree and the oak tree is as follows;

Difference:

Difference is the subtraction of one number from another. Therefore, the distance between the maple tree and the oak tree is the difference between the maple tree to the end and the sum of  oak to pine and pine to the end.

170 / 6 - 58 / 3 = 170 - 116/ 6 = 54 / 6  = 18 / 2 = 9 yards

Therefore,  the distance between the maple tree and the oak tree is 9 yards

learn more on distance here: https://brainly.com/question/26891337

i really need help with my homework and its so hard can you help me plss here is question one m+43=38+46

Answers

Answer:

m = 41

Step-by-step explanation:

m + 43 = 38 + 46

m + 43 = 84 ( subtract 43 from both sides )

m = 41

3.) Simplify the expression by combining like
terms: 45s^2 - 19 - s^2 + 16
please help i’m sick and don’t understand:(

Answers

[tex]45s^2-19-s^2+16\\=45s^2-s^2-19+16\\=s^2(45-1)-19+16\\=44s^2+(-19+16)\\=44s^2-3[/tex]

Hope that helps and hope you get better!

i need help with this​

Answers

Since angle 163 is obtuse we can subtract that from 180 since an obtuse angle + and acute angle with equal 180.
So 180-163 = 17!

Answer: 17 degrees

Step-by-step explanation: Because you have angle A= 163, you can tell that angle B is 17 degrees (sum of angles on one side of a straight line add up to 180). Line M and line N are parallel, so they have corresponding angles, making angle B and angle X are the same. See picture attached for my diagram :). hope this helped!

Jeff had 1 A,4Bs and 2 C's what was he's gpa

Answers

Answer:

Hes Gpa Is that man is good. helps :0

Step-by-step explanation:

Write the algebraic representation when the
scale factor is 8.

Answers

hi, the answer is (8x, 8y)

Here is a system of linear equations
2x+3y=14
4x-3y=10

Which would be more helpful for solving the system: adding the two equations or subtracting one from the other?

Answers

Answer:

adding the 2 equations

Step-by-step explanation:

2x + 3y = 14 → (1)

4x - 3y = 10 → (2)

since the coefficients of the y- terms are opposites then adding will eliminate y

add (1) and (2) term by term

6x + 0 = 24

6x = 24 ( divide both sides by 6 )

x = 4

substitute x = 4 into either of the 2 equations and solve for y

substituting into (1)

2(4) + 3y = 14

8 + 3y = 14 ( subtract 8 from both sides )

3y = 6 ( divide both sides by 3 )

y = 2

solution is (4, 2 )

There are 135 people in a sport centre.
73 people use the gym.
59 people use the swimming pool.
31 people use the track.
19 people use the gym and the pool.
9 people use the pool and the track.
16 people use the gym and the track.
4 people use all three facilities.
Given that a randomly selected person uses at least two facilities, what is the probability they
use all the facilities?

Answers

Answer:

1/9

Step-by-step explanation:

4 people use all three facilities, then

16 - 4 = 12 people use the gym and the track and do not use the pool;

9 - 4 = 5 people use the pool and the track and do not use the gym;

19 - 4 = 15 people use the gym and the pool and do not use the track.

At least two facilities use 4 + 12 + 5 + 15 = 36 people, 4 of them use all three facilities. Thus, the probability that a randomly selected person which uses at least two facilities, uses all the facilities is 4/36 which is equivalent to 1/9

73:59:31:19:9:16:4
the probability of using 2 would be 8

HELP PLEASE i will give 25

Answers

Answer:

130°

.....

....................

Larry is preparing jars of tomatoes from his garden. Each of his three sisters has asked for at least two jars of tomatoes, and Larry needs at least five jars for himself. i need help right now

Answers

if i tell you the truth i dont even know

Directions: Express the number in scientific notation.
The human eye blinks an average of 4,200,000
times a year.

Answers

Answer:

count how many time you need to move the decimal point to only have 1 number on the left

4,200,000 = 6 times

4.2 × 10^6

I need help getting the answer for this one. Thank you

Answers

The next step is to to construct a line through point R  is the option;

Place the compass on point T. without changing the setting from the previous step, draw a small arc above [tex]\overleftrightarrow{ST}[/tex]

What are the steps to construct a perpendicular to a line?

The steps to  construct a perpendicular through the point R are;

Place the compass at point R and draw an arc intersecting the line ST at the point S and T.

Place the compass at point S and draw the arc given in the drawing.

Place the arc at point T and without changing the setting draw an arc above the line ST to intersect the previous arc.

Join the point of intersection of the arcs to the point R to complete the construction of the perpendicular to the line ST passing through R

The step that should be taken next to construct a line through point R that is perpendicular to [tex]\overleftrightarrow{ST}[/tex] is therefore;

Place the compass on point T. without changing the setting from the previous step, draw a small arc above [tex]\overleftrightarrow{ST}[/tex]

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Multiply: (3xl-5)(-x + 4)
)+
Applying the distributive property, the expression becomes (3x)(-x) + (3x)(4) + (-5)(-x) + (-5)(4).
What is the simplified product in standard form?
px +
62 +

Answers

Answer:

Step-by-step explanation:

Multiply: (3x - 5)(-x + 4)

By applying the distributive property,

(3x - 5)(-x + 4)

= (3x)(-x) + (3x)(4) - (5)(-x) - (5)(4)

= -3x^2 + 12x + 5x - 20

= -3x^2 + 17x - 20

That is the simplified product in standard form.

Let's see

[tex]\\ \rm\longmapsto (3x-5)(-x+4)[/tex]

a(b+c)=ab-bc

[tex]\\ \rm\longmapsto 3x(-x+4)-5(-x+4)[/tex]

[tex]\\ \rm\longmapsto -3x^2+12x+5x-20[/tex]

[tex]\\ \rm\longmapsto -3x^2+17x-20[/tex]

What is the opposite operation of squaring? Using this opposite operation, rewrite the equation from question 1 so s is by itself on one side of the equation.

Answers

The opposite operation of squaring is to find the square root. I dunno what the original equation is so I can’t help with that

Consider an urn with 7 black balls, 3 yellow balls, and 4 orange balls. If 3 balls are chosen randomly with replacement, what is the probability that the first is yellow, the second is orange, and the third is orange

Answers

Answer:

1.79% chance or [tex]\frac{6}{343}[/tex]

Step-by-step explanation:

7+3+4=14

chance of yellow [tex]\frac{3}{14}[/tex]

chance of orange [tex]\frac{4}{14}[/tex]

[tex]\frac{3}{14} * \frac{4}{14} *\frac{4}{14} = \frac{6}{343}[/tex]

A group of students must collect at least $150 to organize a science fair. They have already collected $30. Which graph best represents all remaining amounts of money, in dollars, that the students should still collect to organize the science fair?

Number line graph with a closed circle on 120 and shading to the right.
Number line graph with a closed circle on 30 and shading to the right.
Number line graph with a closed circle on 150 and shading to the right.
Number line graph with a closed circle on 180 and shading to the right.

Answers

Answer:

Number line graph with a closed circle on 120 and shading to the right.

Step-by-step explanation:

Because they have collected 30 dollars already and must collect at least 150 dollars, the closed circle would go on 120, going to the right. (150-30=120)

50 POINTS!
The two main parts of an equation in Slope-Intercept Forrn are the Slope and the Y-Intercept.

A. True

B. False

Answers

Answer:

A

Step-by-step explanation:


Solve for m:
(-11/6) + m = -2/9
M=

Answers

Step-by-step explanation:

(-11/6) + m = -2/9

m = -2/9 + 11/6

the last common multiple of 9 and 6 is 18.

so, we are bringing both fractions to .../18.

m = -2×2/18 + 11×3/18 = -4/18 + 33/18 = 29/18

A) 22.4
B) 43.7
C) 85.3
D) 4.75

Answers

The answer is approximately b and the wrong answers are A C and D you’re welcome make sure you give me 5 stars

Answer:

its should be b

Step-by-step explanation

mark brainlist

PLEASE HURRY I NEED HELP

Answers

Answer:

I think 58% I’m not 100% sure but yea

Step-by-step explanation:

I divided the number of votes for printed 71 by the total number of votes 122 so 71/122=.58 58%

Let g(x) = 3(x - 6)^2 + 1. Find the range of $g$.

Answers

Answer:

[1,∞)

Step-by-step explanation:

Let's try to plug in some numbers.

When solving a problem fo range, the best place to start is where you can let the (x - b) part = 0.

This is what I mean

3(x-6)² + 1

Let x = 6

3(0)² + 1 = 1

Look how we have a 0 inside the parentheses.

That's what I mean.

Now let's try using terms smaller than 6.

Now, let's try plugging in 5

3(-1)² + 1 = 4

Now try plugging in 4

3(-2)² + 1 = 13

Looks like we will just keep going up.

Now let's try using terms bigger than 6.

Plugging in 7

3(1)² + 1 = 4

Plugging in 8

3(2)² + 1 = 13

We just go up both ways because of the x squared term.

So our smallest value is at x = 6 where we have y = 1.

If we go either direction forever to the right or left the terms to get bigger, where it approaches infinity.

So, 1 will have parentheses as it can be reached and infinity will have parentheses as it is unreachable and goes on forever.

[1,∞)

Part A: What do the x-intercepts and maximum value of the graph represent in context of the described situation?
Part B: What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and
profit for the company in the situation described?
Part C: What is an approximate average rate of change of the graph from x = 1 to x = 3, and what does this rate represent in
context of the described situation?

Answers

The x intercept of the given graph of the company's profit is where the curve of the graph crosses the x-axis.

How to determine the x-intercept

In this figure, the graph crosses the x-axis at x = 0 and x = 6

This represents the profit is 0 when the price is $0 and $6, respectively

The maximum value

This represents the maximum profit that can be made.

From the graph, the maximum profit is $120

The increasing and the decreasing interval

From the graph, the graph increases from x = 0 to x = x = 3, and it decreases from x = 3 to x = 6

These intervals represent when the profit increases, and when it decreases

The average rate of change

This is calculated as:

[tex]m = \frac{f(b) - f(a)}{b - a}[/tex]

So, we have:

[tex]m = \frac{f(3) - f(1)}{3 - 1}[/tex]

[tex]m = \frac{f(3) - f(1)}{2}[/tex]

Substitute known values

[tex]m = \frac{120 - 60}{2}[/tex]

[tex]m = \frac{60}{2}[/tex]

Simplify

[tex]m = 30[/tex]

Hence, the average rate of change from x = 1 to x = 3 is a profit of $30 per unit sale

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In a toy​ store, the ratio of the number of teddy bears to the number of dolls is 7:3 . If the store has 140 teddy bears ​, how many dolls are in the​ store?

Answers

Answer:

I prefer to set their units in order so it can help me;

Bears/Dolls

7 Bears     140 bears

_______ = _______

3 Dolls               x

⇒ 7 Bears   x20  140 bears

   _______    =    _______ , 3(20) = 60 Dolls

    3 Dolls     x20         x

Your odometer reads 4,261 miles. You drive your car until the odometer reads 4,751 and your car used 25 gallons of gasoline during the trip.
About how many miles per gallon has your car been getting? Round up to the highest ten.

20
35
170
190

Answers

Answer:

35 gallons.

Step-by-step explanation:

Why? Bc it is the closest 4,751

good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.

Answers

Answer:

Based on the linear regression equation, the intercept means that for 0 missed classes, the expected test score is 98✓

we know that,

y intercept exist when x = 0

so,

⇢y = -4x +98

⇢y = -4 x 0 +98

⇢y = 98

so , the expected test score is 98

Based on the linear regression equation, the slope means that for every missed class, the expected tast score decreases by 4 points✓

when x = 0

y = -4(0) +98

when x = 1

y= -4(1) +98 = 94

when x = 2

y= -4(2) +98 = 90

we can see the decresement of 4 points

Based on the linear regression equation, as the number of days a student misses class increases the expected test score decreases ✓

We can see that the increament in absent days lead to lower scores ( one class = 4 points)

y=-4x+98

For 0 clases

y=-0+98=98

Option A is certified as correct

Here slope is -4

So it decreasing not increasing

Option C is correct

Yes as the missed classes increase expected test decreasing as slope is negative.

Option F is correct

Which expressions represent the total area of the large rectangle.

Answers

Answer:

a, c, and e represent the total area

Answer:

(m+n)*6

Step-by-step explanation:

The total area of a rectangle= length*breath

So using this,

Length (l)=n+m

Breath (b)= 6

We know that,

Area of rectangle (A)=l*b

=(n+m)*6

=(n+m)6

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