Consider the equation px^2 + qx + r = 0,where | vedclass

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(D) Let the roots of the quadratic equation $px^2 + qx + r = 0$ be $\alpha$ and $-\alpha$.According to the properties of roots,the sum of the roots is

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$q = 0, pr < 0$

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(D) Let the roots of the quadratic equation $px^2 + qx + r = 0$ be $\alpha$ and $-\alpha$.According to the properties of roots,the sum of the roots is given by $-\frac{q}{p}$.Since the roots are $\alpha$ and $-\alpha$,their sum is $\alpha + (-\alpha) = 0$.Therefore,$-\frac{q}{p} = 0$,which implies $q = 0$.For the roots to be real and non-zero (as they have opposite signs),the discriminant $D = q^2 - 4pr$ must be greater than $0$.Substituting $q = 0$,we get $D = 0^2 - 4pr = -4pr$.For $D > 0$,we must have $-4pr > 0$,which implies $pr Thus,the condition is $q = 0$ and $pr < 0$.

Consider the equation $px^2 + qx + r = 0$,where $p, q, r$ are real. The roots are equal in magnitude but opposite in sign when

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