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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Updated on: 10-Oct-2022

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