If $9 x^{2} + k x + 1 = 0$ has equal roots, find the value of $k$ .

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Solution

The given equation if $9 x^{2} + k x + 1 = 0$
comparing with $a x^{2} + b x + c = 0$
here $a = 9$ , $b = k$ , $c = 1$
$△$ = $b^{2} - 4 a c$
= $k^{2} - 4 (9) (1)$
= $k^{2} - 36$
The roots are equal so $△$ must be zero
$∴$ = $k^{2} - 36 = 0$
= $(x + 6) (x - 6) = 0$
= $x + 6 = 0$ or $x - 6 = 0$
$∴$ $k = - 6$ or $k = 6$

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