Question

Find the values of p for which the quadratic equation 4x+px+3=0 has equal roots

Answer 1

HI !

4x + px + 3 = 0
a = 4 , b = p  , c = 3

As the equation has equal roots ,
b² - 4ac = 0

p² - 4 × 4 × 3 = 0

p² - 48 = 0

p² = 48

p = √48

p = 4√3

Answer 2

Given:

A quadratic equation

$4 {x}^{2} + px + 3 = 0$

To find:

The values of p for which the given quadratic equation has equal roots.

Solution:

The values of p for which given quadratic equation has equal roots is 4√3 and -4√3.

To answer this question, we will follow the following steps:

As we know in a quadratic equation,

$a {x}^{2} + bx + c = 0$

the a and b are coefficients of x2 and x respectively.

Also, if the above quadratic equation has equal roots then

${b}^{2} - 4ac = 0$

Now,

As given, we have a quadratic equation,

$4 {x}^{2} + px + 3 = 0$

Where

a = 4, b = p and c = 3

So,

For equal roots

${p}^{2} - 4(4)(3) = 0$

${p}^{2} - 48 = 0$

${p}^{2} = 48$

$p = 4 \sqrt{3} \: and \: - 4 \sqrt{3}$

Hence, for equal roots, the values of p are 4√3 and -4√3.