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Nature of Roots

For what valu...

Question

For what value/values of $k$ :
$(k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0$ has equal roots

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Solution

Condition to have equal roots
$b^{2} = 4 a c 4 (3 k + 1)^{2} = 4 (k + 1) (8 k + 1) 9 k^{2} + 6 k + 1 = 8 k^{2} + 9 k + 1 k^{2} = 3 k k = 0, 3$

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Find the value of k for which the quadratic equation $(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0$ has equal roots. Also, find the roots.

(3 k + 1) x^{2} + 2 (k + 1) x + 1 = 0

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