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

$kx^2 - 2\sqrt5x + 4 = 0$

Given:

Given quadratic equation is $kx^2 - 2\sqrt5x + 4 = 0$.

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,

$a=k, b=-2\sqrt5$ and $c=4$.

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

$D=(-2\sqrt5)^2-4(k)(4)$

$D=4(5)-16k$

$D=20-16k$

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

Therefore,

$20-16k=0$

$16k=20$

$k=\frac{20}{16}$

$k=\frac{5}{4}$

The value of $k$ is $\frac{5}{4}$.

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Updated on: 10-Oct-2022

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