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Nature of Roots

If the roots ...

Question

If the roots of the equation $x^{2} - (p + 4) x + 2 p + 5 = 0$ are equal, then the value(s) of $p$ is/are

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Solution

The correct options are
A $2$
C $- 2$
$x^{2} - (p + 4) x + 2 p + 5 = 0$
As roots are equal, so
$D = 0 \Rightarrow (p + 4)^{2} - 4 (2 p + 5) = 0 \Rightarrow p^{2} + 8 p + 16 - 8 p - 20 = 0 \Rightarrow p^{2} - 4 = 0 \Rightarrow p = \pm 2$

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