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  4. If difference of roots of the equation x2-p x+q=0 is 1 , then p2+4 q2 equals -

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Q. If difference of roots of the equation $x^2-p x+q=0$ is 1 , then $p^2+4 q^2$ equals -

Complex Numbers and Quadratic Equations

Solution:

$x^2-p x+q=$ image $\alpha-\beta=1$
$(\alpha+\beta)^2-4 \alpha \beta=(1)^2$
$p^2-4 q=1$........(i)
$\Rightarrow $ from (i)
$p^2=1+4 q$
$1+4 q+4 q^2=(2 q+1)^2$