If the ratio of the roots of the equation ax^ | vedclass

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(B) Let the roots of the equation $ax^2 + bx + c = 0$ be $p\alpha$ and $q\alpha$.From the relationship between roots and coefficients:$p\alpha + q\alp

Vedclass · Accepted Answer

$pqb^2 - (p + q)^2ac = 0$

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(B) Let the roots of the equation $ax^2 + bx + c = 0$ be $p\alpha$ and $q\alpha$.From the relationship between roots and coefficients:$p\alpha + q\alpha = -\frac{b}{a} \implies \alpha(p + q) = -\frac{b}{a} \implies \alpha = -\frac{b}{a(p + q)}$Also,$p\alpha \cdot q\alpha = \frac{c}{a} \implies pq\alpha^2 = \frac{c}{a}$Substituting the value of $\alpha$ in the second equation:$pq \left( -\frac{b}{a(p + q)} \right)^2 = \frac{c}{a}$$pq \cdot \frac{b^2}{a^2(p + q)^2} = \frac{c}{a}$Multiplying both sides by $a^2(p + q)^2$:$pqb^2 = ac(p + q)^2$$pqb^2 - (p + q)^2ac = 0$

If the ratio of the roots of the equation $ax^2 + bx + c = 0$ is $p:q$,then

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