If p and q are the roots of the equation x^{2 | vedclass

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(A) Given that $p$ and $q$ are the roots of the quadratic equation $x^{2}+px+q=0$.According to the relation between roots and coefficients:Sum of root

Vedclass · Accepted Answer

$p=1, q=-2$

Vedclass · Answer

(A) Given that $p$ and $q$ are the roots of the quadratic equation $x^{2}+px+q=0$.According to the relation between roots and coefficients:Sum of roots: $p+q = -p \Rightarrow 2p+q=0$ (Equation $1$)Product of roots: $pq = q$ (Equation $2$)From Equation $2$, $pq - q = 0 \Rightarrow q(p-1) = 0$.This implies either $q=0$ or $p=1$.Case $I$: If $q=0$, then from Equation $1$, $2p+0=0 \Rightarrow p=0$. However, if $p=0$ and $q=0$, the equation becomes $x^2=0$, which has roots $0, 0$. This is a valid solution, but let us check the options.Case $II$: If $p=1$, then from Equation $1$, $2(1)+q=0 \Rightarrow q=-2$.Thus, the pair $(p, q) = (1, -2)$ satisfies the given condition.

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

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