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Location of Roots

Find the valu...

Question

Find the value of p+q if the equation $x^{2} + (p + q) x +$ $\frac{p q}{b}$ =0 has equal roots. ___

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Solution

$△ = 0$
$\Rightarrow (p + q)^{2} - 4$ x $\frac{p q}{2}$ =0
$\Rightarrow p^{2} + q^{2} + 2 p q - 2 p q = 0$
$\Rightarrow p^{2} + q^{2} = 0$
$\Rightarrow$ p=0 and q=0
$\Rightarrow$ p+q=0

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