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

$3x^2 - 5x + 2k = 0$

Given:

Given quadratic equation is $3x^2 - 5x + 2k = 0$.

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,

$a=3, b=-5$ and $c=2k$.

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

$D=(-5)^2-4(3)(2k)$

$D=25-24k$

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

Therefore,

$25-24k=0$

$24k=25$

$k=\frac{25}{24}$

The value of $k$ is $\frac{25}{24}$.

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Updated on: 10-Oct-2022

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