Question

find the value of k. in quadratic equation 9x2-kx+16=0 if roots are equal​

Answer 1

Answer:

k=24,k=-24

Step-by-step explanation:

may this answer was helpful

Answer 2

Given:

A quadratic equation 9x2-kx+16=0 in which roots are equal.

To find:

The value of k.

Solution:

To answer this question, first of all, we should know that if a quadratic equation

${ax}^{2} + bx + c = 0$

has equal roots then

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

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

Now, as given,

we have a quadratic equation

${9x}^{2} - kx + 16 = 0$

Where b = -k

a = 9 and c = 16

As the roots of this quadratic equation are equal

so,

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

${(-k)}^{2} - 4(9)(16) = 0$

${k}^{2} - 576 = 0$

${k}^{2} = 576$

On taking square root on both sides, we have

$k = \sqrt{576}$

$k = + 24 \: and \: - 24$

Hence, the value of k is +24 and -24.