If $x^{2} - 2 p x + 8 p - 15 = 0$ has equal roots, then $p =$

3

- 5

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3

5

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- 3

5

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- 3

- 5

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Solution

The correct option is B $3$ or $5$
Given equation is $x^{2} - 2 p x + 8 p - 15 = 0$
Here $a = 1, b = - 2 p, c = 8 p - 15$
We know for equal roots, $b^{2} - 4 a c = 0$
Therefore, $(- 2 p)^{2} - 4 (1) (8 p - 15) = 0$
$\Rightarrow 4 p^{2} - 32 p + 60 = 0$
$\Rightarrow p^{2} - 8 p + 15 = 0$
$\Rightarrow (p - 5) (p - 3) = 0$
i.e., $p = 5$ or $3$

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