Find the value/values of p , if the equation $x^{2} + p x + 25 = 0$ has real and equal roots.

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Solution

The correct options are
C 10
D -10
When you compare the given equation to the standard form $a x^{2} + b x + c = 0$ we get,
$a = 1, b = p a n d c = 25$
Given that , the roots of the equation are real and equal.
i.e. , D = 0
$\Rightarrow D = b^{2} - 4 a c = p^{2} - (4 \times 1 \times 25) = 0$
$\Rightarrow p^{2} - 100 = 0$
$\Rightarrow p^{2} = 100$
$∴ p = 10 o r - 10$

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