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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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