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Find the values of k for which the roots are real and equal in each of the following equations:
$(k+1)x^2 - 2(3k+1)x + 8k+1 = 0$
Given quadratic equation is $(k+1)x^2 - 2(3k+1)x + 8k+1 = 0$.
We have to find the values of k for which the roots are real and equal.
Comparing the given quadratic equation with the standard form of the quadratic equation $ax^2+bx+c=0$, we get,
$a=k+1, b=-2(3k+1)$ and $c=8k+1$.
The discriminant of the standard form of the quadratic equation $ax^2+bx+c=0$ is $D=b^2-4ac$.
The given quadratic equation has real and equal roots if $D=0$.
$k=0$ or $k-3=0$
$k=0$ or $k=3$
The values of $k$ are $0$ and $3$.
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