For what value of 'k' the equation $(k + 3) x^{2} - (5 - k) x + 1 = 0$ has coincident roots ?

1, 13

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1, 12

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3, 13

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None of these

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Solution

The correct option is B $1, 13$
For coincident roots, $D = 0$
Now, ${[- (5 - k)]}^{2} - 4 \times (k + 3) \times 1 = 0$
$\Rightarrow 25 + k^{2} - 10 k - 4 k - 12 = 0$
$\Rightarrow k^{2} - 14 k + 13 = 0$
$\Rightarrow (k - 13) (k - 1) = 0$
$∴ k = 13, 1$

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