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

$kx^2 + 4x + 1 = 0$

Given:

Given quadratic equation is $kx^2 + 4x + 1 = 0$.

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,

$a=k, b=4$ and $c=1$.

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

$D=(4)^2-4(k)(1)$

$D=16-4k$

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

Therefore,

$16-4k=0$

$4k=16$

$k=\frac{16}{4}$

$k=4$

The value of $k$ is $4$.

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Updated on: 10-Oct-2022

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