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

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Solution

$\Rightarrow (3 - k) x^{2} + 1 = 0$
Roots are equal $\Rightarrow Δ = 0$
$\Rightarrow b^{2} - 4 a c = 0$ where $b = 0, a = 3 - k, c = 1$
$\Rightarrow - 4 \times (3 - k) \times 1 = 0$
$\Rightarrow k - 3 = 0$
$∴ k = 3$

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