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

$4x^2 - 3kx + 1 = 0$

Given:

Given quadratic equation is $4x^2 - 3kx + 1 = 0$.

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,

$a=4, b=-3k$ and $c=1$.

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

$D=(-3k)^2-4(4)(1)$

$D=9k^2-16$

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

Therefore,

$9k^2-16=0$

$9k^2=16$

$k^2=\frac{16}{9}$

$k=\sqrt{\frac{16}{9}}$

$k=\pm \frac{4}{3}$

The values of $k$ are $-\frac{4}{3}$ and $\frac{4}{3}$.

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Updated on: 10-Oct-2022

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