If a(p + q)^2 + 2bpq + c = 0 and a(p + r)^2 + | vedclass

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(A) Given equations are $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$.These equations imply that $q$ and $r$ are the roots of the quadra

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$p^2 + \frac{c}{a}$

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(A) Given equations are $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$.These equations imply that $q$ and $r$ are the roots of the quadratic equation in $x$:$a(p + x)^2 + 2bpx + c = 0$.Expanding the equation: $a(p^2 + 2px + x^2) + 2bpx + c = 0$.$ax^2 + 2apx + ap^2 + 2bpx + c = 0$.Rearranging in terms of $x$: $ax^2 + 2x(ap + bp) + (ap^2 + c) = 0$.$ax^2 + 2px(a + b) + (ap^2 + c) = 0$.For a quadratic equation $Ax^2 + Bx + C = 0$,the product of roots is given by $\frac{C}{A}$.Here,$A = a$,$B = 2p(a + b)$,and $C = ap^2 + c$.Therefore,the product of roots $qr = \frac{ap^2 + c}{a} = p^2 + \frac{c}{a}$.

If $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$,then $qr$ =

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