Find the values of k for which the roots are real and equal in each of the following equations:

$4x^2 + kx + 9 = 0$

Given:

Given quadratic equation is $4x^2 + kx + 9 = 0$.

To do:

We have to find the values of k for which the roots are real and equal.

Solution:

Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,

$a=4, b=k$ and $c=9$.

The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.

$D=(k)^2-4(4)(9)$

$D=k^2-144$

The given quadratic equation has real and equal roots if $D=0$.

Therefore,

$k^2-144=0$

$k^2=144$

$k=\sqrt{144}$

$k=\pm 12$

The values of $k$ are $-12$ and $12$.

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Updated on: 10-Oct-2022

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