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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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