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

$9x^2 - 24x + k = 0$

Given:

Given quadratic equation is $9x^2 - 24x + k = 0$.

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,

$a=9, b=-24$ and $c=k$.

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

$D=(-24)^2-4(9)(k)$

$D=576-36k$

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

Therefore,

$576-36k=0$

$36k=576$

$k=\frac{576}{36}$

$k=16$

The value of $k$ is $16$. 

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Updated on: 10-Oct-2022

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