find the values of P for which the quadratic equation 4x²+px+3=0?​

Answers

Answer 1
Correct Questions :-

Find the values of P for which the quadratic equation 4x²+px+3=0 , provided that roots are equal or discriminant is zero .

Solution:-

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.

For equal roots

D = 0

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

So,

[tex]\sf{ β² - 4αc = 0}[/tex]

Here,

α = 4β = pc = 3

Now,

[tex]\begin{gathered}\implies\quad \sf p²- 4 \times 4 \times 3 =0 \end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf p²- 48 =0 \end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf p²=48\end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf p=±\sqrt{48}\end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \sf p=±\sqrt{2 \times 2 \times 2 \times 2 \times 3} \end{gathered}[/tex]

[tex]\begin{gathered}\implies\quad \sf p=± 2\times 2\sqrt{ 3 }\end{gathered} [/tex]

[tex]\begin{gathered}\implies\quad \boxed{\sf{p=±4\sqrt{ 3 }}}\end{gathered} [/tex]

Thus, the values of P for which the quadratic equation 4x²+px+3=0 are-

4√3 and -4√3.


Related Questions

evaluate each question

-12 • (-1/3)

Answers

Answer:

4

Step-by-step explanation:

[tex] = - 12 \times ( \frac{ - 1}{3} ) \\ = \frac{12}{3} \\ = 4[/tex]

- 12 × -1 is +12 because - × - = +

What is the area of this triangle?

Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answers

Answer:   48.6

=======================================================

Work Shown:

area = 0.5*side1*side2*sin(angle)

area = 0.5*13*7.5*sin(94)

area = 48.6312474501664

area = 48.6 square inches

Notes:

Make sure your calculator is in degree mode.The angle must be between the two sides mentioned. For more info, check out the SAS triangle area formula.

Answer: 48.6

Step-by-step explanation:

i took the test

If I have 1 apple, and I get 2 apples, how many apples do I have

Answers

Answer:

you have 1

you get 2

2+1=3

You now have 3 apples :)

Hey!

you have 3 apples.

2+1 is 3.

Ellie is making a batch of pancakesand her recipe calls for 1 1/2 cups offlour and 1 1/4 cups of milk. If she only has 1 cup of milk, how much flour should she use to make the same pancake recipe?

Answers

Answer: 6 cups

Step-by-step explanation:

multiple the 1 1/2 by 4

Solve this quickly please!!

Answers

Answer:

Step-by-step explanation: we will first work out a

so 23 is the hypotenuse

a is the opposite

so what we need to do is 46sin(23) and that will give you 17.97 cm

next we will work out b

b is the adjacent

23 is the hypotenuse

so in this case we must do 46cos(23) and that will give you 42.34

last, we will work out B

a is 17.97 cm and its the adjacent

23 is the hypotenuse

so we do sin-1(17.97/23)= 51.38

calculate the area of the figure below​

Answers

Answer:

164 cm²

Step-by-step explanation:

Take the 2 shapes and find the areas

Triangle area = (bh)/2

                          13 × 8 × 0.5 = 52

Rectangle area = 16 × 7 = 112

Add up the areas

112 + 52 = 164

Answer:

136 cm²

Step-by-step explanation:

The composite figure is made up of a triangle and a rectangle.

Area of the triangle

[tex]\boxed{\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\ \implies \textsf{Area of $\triangle ABD$}&=\dfrac{1}{2} \times BD \times AB\\&=\dfrac{1}{2} \times (16-8) \times (13-7)\\&=\dfrac{1}{2} \times 8 \times 6\\&=4 \times 6\\&=24\; \sf cm^2\end{aligned}}[/tex]

Area of the rectangle

[tex]\boxed{\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\\\ \implies \textsf{Area of rectangle $BCFE$}&= EF \times CF\\&=7 \times 16\\&=112\; \sf cm^2\end{aligned}}[/tex]

Therefore, the area of the composite figure is:

[tex]\boxed{\begin{aligned}\textsf{Area of the composite figure}&=\sf Triangle + Rectangle\\ & = 24 + 112\\&=136\; \sf cm^2\end{aligned}}[/tex]

The price per mp3 download 5 years ago was $0.99. Now, each mp3 download costs $1.29. Which statement is true?

Answers

Answer:

inflation?

Step-by-step explanation:

nothing here

Answer:

that would be an example of inflation.

I noticed your question was not complete, so I hope this helps you as much as possible.


answer for a lot of points !!!

Answers

Answer:

ABABCC

Step-by-step explanation:

DEFINITION: A rhyme scheme the ordered pattern of rhymes at the ends of the lines of a poem or verse (according to the Oxford Dictionary)

Cloud is the first rhyme in the sentence, in which we call A.

Hills doesn't rhyme with cloud, so it is B.

Crowd rhymes with cloud, so we call it A.

Daffodils rhyme with hills, so we make it B.

Trees doesn't rhyme with anything else, so we call it C.

Breeze rhymes with trees, so we make it C.

Answer: Ok the awnser is AABBCC and also its only five points but i will take it! happy christmas!!!!

Two number whose product is -168 and sum is -13

Answers

Answer:

-21 and 8

Step-by-step explanation:

-21 × 8 = -168 and -21 + 8 = -13

Hope this helps!

Given the definitions of f(x) and g(x) below, find the value of (gof)(-1).
f(x)=x^2+3x+1
g(x)=x-4

Answers

Answer:

f(x)_x^3x+2+1

f(x)=3x+3

g(x)_4x

find H.C.F. of 144, 252 and 630​

Answers

The HCF IS 18

HOPE THIS HELPS U

What is the value of h(3)?
o -2
0 -11
0 1
O 2

Answers

Answer:

h(3) = 1

Step-by-step explanation:

See attached image.

find the volume of the cone

Answers

The volume of the cone is [tex]\frac{1}{3} \pi r^{2} h[/tex]

r: radius --> 3fth: height --> 12ft [tex]\pi\\[/tex] = 3.14

Volume =  [tex]\frac{1}{3} \pi *(3)^{2} *12 = 113.04ft^3[/tex]

Hope that helps!

A box of alexanders is in form of prism rectangular it is measured 13 longitud, 8 of widht, and 4.8 of height, what is the area total, area lateral and area without of one of the edges of __ (Dont know the underlined)

Answers

Answer:

lateral area and area without one side: 20.8

Jan rewrote the expression ½y • 5 as 5 •½y Which property of operations did Jan use?​

Answers

Answer:

Commutative property of multiplication

Step-by-step explanation:

Answer:

Jan is using commutative property.

Step-by-step explanation:

Commutative property is when you switch values and they don't make a change in the outcome.

Just remember, this only applies to addition and multiplication but does not apply to division or subtraction!!!

Examples:

2+4=6

4+2=6

9x3=27

3x9=27

use the values to solve this problem a=4 b=2, c=5 9a-(4b+2c)

Answers

Answer:

36 is the answer !!

Step-by-step explanation:

9(4)-(4(2) + 2(5))

36-8+10

26+10

36

Which figures show adjacent angles

Answers

i think it would be 2 and 3 not too sure though

this is a sketch of the curve with equation y=f(X). The curve has a minimum point at M(-1,-3).

Answers

The minimum point of the function y=f(x)+3 is at (-1 , 0 ) .

The biggest and lowest value of a function, either inside a specific range (the local or relative extrema) or on the entire domain, are generally referred to as extrema (plural of extremum) in mathematical analysis (the global or absolute extrema). One of the first mathematicians to suggest the general method of adequacy for determining the maxima and minima of functions was Pierre de Fermat.

The maximum and minimum of a set are the greatest and least items in the set, as described by set theory. There are no minimum or maximum values in unbounded infinite sets, such as the set of real numbers.

Say that (x,y) = where y = f(x) minimum occurs at (-1,-3). As a result, for all other x inside its domain of definition, y= f(x) >=-3

y = f(x) + 3 simply elevates the graph of y by 3 and increases the value of y for any x. Its minimum x-value remains at -1, and its value for y is f(3) + 3 = -3 + 3 = 0. as a result, new minimum =(-1 , 0 ) .

To learn more about maximum and minimum values of a function visit:

https://brainly.com/question/13581879

Disclaimer: The complete question is :

This is a sketch of the curve with equation y=f(X). The curve has a minimum point at M(-1,-3).Find the minimum value for the function y=f(x)+3 .

#SPJ1

Which set of ordered pairs represents a function?
O{(-5, -1), (9,7).(-2,6),(-3,7)}
O{(-7,5),(-9,-4),(-3,-1),(-3,4)}
O{(5,-3), (1,2), (1,8),(4,6)}
O{(-2,9), (-2, 6), (1, -5), (-4,-8)}
Submit Answer

Answers

a function set does not contain any X-repeats, or namely that the x-coordinate on every pair is different, let's take a peek at these sets, Check the picture below.

Jimmy is having a birthday party at the zoo. The zoio has a fixed fee for birthday parties, plus a fee per person. Jimmy is told the total charge for ten people,including himself, would be 97. 50 and the total charge for 20 people, including himself would be $175. Determine the independent and dependent variable

Answers

Answer:

independent: number of personsdependent: charges

Step-by-step explanation:

The scenario describes charges as being dependent on the number of persons. That means the independent variable is the number of persons, and the dependent variable is the total charge.

(When we say "A depends on B", that automatically defines A as being the dependent variable, and B the independent variable.)

__

Additional comment

Perhaps you also want to know the relationship between the charges c and the number of persons p. That will be ...

  c = 7.80p +19.00

You know the rate per person from the fact that adding 10 people to the party raises the cost by $78. Then the 10-person charge includes a fixed fee of $97 -78 = $19.

there are 45 boys on the track team. About 25% of the boys were on the team last year. About how many boys were on the track team last year

Answers

Answer:

about 11 boys were on the track team last year.

Roughly approximately about 11-1/4 of fhem.

Can anyone explain me well thats whats
" twice the variable P divided by the product of 5 and q

Answers

Answer:

See below.

Step-by-step explanation:

Twice means multiplied by 2.

Product is the solution to a multiplication equation.

2p/5q

-hope it helps

Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).

Answers

Answer:

The answer is A.

Step-by-step explanation:

Took it on Edge (:

using a ruler and a pair of compass only construct triangle XYZ such that XY=9.5
<YXZ=60

Answers

Answer: 22.5

Explanation: from P the radii of length r are perpendicular to xz, xy, and yz and all the same.

if draw it with your compass your see a certain symmetry

call the tangent point on xz Q and the one on xy S

triangle XQP is congruent to XSP and is a right triangle

the two angles at x are 22.5 degrees

so PQ = PS = 4 tan 22.5

A forest ranger collected data about the rainfall in a forest, in inches, on consecutive days of a month. His data is shown using the dot plot. Create a box plot to represent the data. dot plot titled Monthly Rainfall and number line from 2 to 3 in increments of 1 tenth labeled Rainfall (in inches) with zero dots over 2, zero dots over 2 and 1 tenth, zero dots over 2 and 2 tenths, 1 dot over 2 and 3 tenths, 2 dots over 2 and 4 tenths, 1 dot over 2 and 5 tenths, 2 dots over 2 and 6 tenths, 2 dots over 2 and 7 tenths, 2 dots over 2 and 8 tenths, zero dots over 2 and 9 tenths, and zero dots over 3 box plot with minimum value 2 and 3 tenths, lower quartile 2 and 4 tenths, median 2 and 6 tenths, upper quartile 2 and 7 tenths, and maximum value 2 and 8 tenths box plot with minimum value 2 and 2 tenths, lower quartile 2 and 4 tenths, median 2 and 6 tenths, upper quartile 2 and 7 tenths, and maximum value 2 and 8 tenths box plot with minimum value 2 and 3 tenths, lower quartile 2 and 4 tenths, median 2 and 5 tenths, upper quartile 2 and 7 tenths, and maximum value 2 and 8 tenths box plot with minimum value 2 and 2 tenths, lower quartile 2 and 4 tenths, median 2 and 5 tenths, upper quartile 2 and 6 tenths, and maximum value 2 and 8 tenths

Answers

The box plot showing the five-number summary of the data in the dot plot is shown in the image attached below (see attachment).

What is a Box Plot?

A box plot shows the five-number summary of a data distribution which includes:

Minimum valueMaximum valueMedianUpper quartile (Q3)Lower quartile (Q1)

To create a a box plot for the data, we need to state out each data point given in the dot plot, which are:

2.3, 2.4, 2.4, 2.5, 2.6, 2.6, 2.7, 2.7, 2.8, 2.8

The five-number summary of the data points stated above would be:

Minimum value - 2.3Maximum value - 2.8Median - 2.6Upper quartile (Q3) - 2.7Lower quartile (Q1) - 2.4

Therefore, the box plot showing the five-number summary of the data in the dot plot is shown in the image attached below (see attachment).

Learn more about box plot on:

https://brainly.com/question/14277132

Answer:

other guy is right

Step-by-step explanation:

Please help me! This is finding slope btw

Answers

Step-by-step explanation:

for number 8. The slope is -3 because the standard form equation is y=mx+c. And we know that m represents your slope.

Hence why it is -3.

For number 10. The slope is 0. I Forgot to write that on the pic

:)

Need help I’m suck on this problem

Answers

This I correct because once anything is to the power of 0 it becomes 1 so you left with 3x5x3x5to the 2nd power, after calculating that you have 9x5to the third=9x125=1125.

Jacques deposited $1,900 into an account that earns 4% interest compounded semiannually. After t years, Jacques has $3,875. 79 in the account. Assuming he made no additional deposits or withdrawals, how long was the money in the account?.

Answers

Answer:

T=50.99

Step-by-step explanation:

Given:

I=3,875.78

P=1,900

R=4% I.e 4/100 , 0.04

T=?

I=PRT

3,875.79=($1,900)(0.04)t

3,875.79=76t

3,875.79/76= t

T=50.99

How could you use subtraction to find the area of a figure

Answers

Answer:

https://brainly.com/question/7699717

Step-by-step explanation:

Solve t(t+4)-1=t(t+2)+2 please show your work

Answers

Answer: T= 3/2

Step-by-step explanation:  t(t+4)-1=t(t+2)+2 simplify into t2+4t−1=t2+2t+2 now subtract t^2=t2+4t−1−t2=t2+2t+2−t2 subtract 2t(both sides)  4t−1=2t+2 2t−1=2=2t−1=2 now add 1 to both sides = 2t−1+1=2+1 than 2t=3 now divide by 2(both sides)= T= 3/2

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