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Find the values of k for which the roots are real and equal in each of the following equations:
$2kx^2 - 40x + 25 = 0$
Given:
Given quadratic equation is $2kx^2 - 40x + 25 = 0$.
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,
$a=2k, b=-40$ and $c=25$.
The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.
$D=(-40)^2-4(2k)(25)$
$D=1600-200k$
The given quadratic equation has real and equal roots if $D=0$.
Therefore,
$1600-200k=0$
$200k=1600$
$k=\frac{1600}{200}$
$k=8$
The value of $k$ is $8$.
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