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Higher Order Equations

If the roots ...

Question

If the roots of $(k + 1) x^{2} - 2 (k - 1) x + 1 = 0$ are real and equal, then find the value of $k$ .

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Solution

$(k + 1) x^{2} - 2 (k - 1) x + 1 = 0$
Since roots are equal then Discriminant $= 0$
$4 (k - 1)^{2} - 4 (k + 1) = 0$
$k^{2} - 3 k = 0$
$k (k - 3) = 0$
then $k = 0$ & $k = 3$ .

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