If p and q are the roots of x^2 + px + q = 0, | vedclass

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Question

(A) For the quadratic equation $x^2 + px + q = 0$,the sum of the roots is given by $p + q = -p$ and the product of the roots is given by $pq = q$.From

Vedclass · Accepted Answer

$p = 1, q = -2$

Vedclass · Answer

(A) For the quadratic equation $x^2 + px + q = 0$,the sum of the roots is given by $p + q = -p$ and the product of the roots is given by $pq = q$.From the product of roots equation: $pq - q = 0 \Rightarrow q(p - 1) = 0$.This implies either $q = 0$ or $p = 1$.Case $1$: If $q = 0$,then the sum of roots equation $p + q = -p$ becomes $p + 0 = -p$,which implies $2p = 0$,so $p = 0$. Thus,$(p, q) = (0, 0)$.Case $2$: If $p = 1$,then the sum of roots equation $p + q = -p$ becomes $1 + q = -1$,which implies $q = -2$. Thus,$(p, q) = (1, -2)$.Comparing with the given options,the correct pair is $p = 1, q = -2$.

If $p$ and $q$ are the roots of $x^2 + px + q = 0$,then

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