If the roots of the equation ax^2 + bx + c = | vedclass

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(B) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $l$ and $2l$.Using the relationship between roots and coefficients:Sum of roots: $l +

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$2b^2 = 9ac$

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(B) Given the quadratic equation $ax^2 + bx + c = 0$ with roots $l$ and $2l$.Using the relationship between roots and coefficients:Sum of roots: $l + 2l = -\frac{b}{a} \Rightarrow 3l = -\frac{b}{a} \Rightarrow l = -\frac{b}{3a}$.....$(i)$Product of roots: $l \cdot 2l = \frac{c}{a} \Rightarrow 2l^2 = \frac{c}{a}$.....$(ii)$Substitute $(i)$ into $(ii)$:$2\left(-\frac{b}{3a}\right)^2 = \frac{c}{a}$$2\left(\frac{b^2}{9a^2}\right) = \frac{c}{a}$$\frac{2b^2}{9a^2} = \frac{c}{a}$$2b^2 = 9ac$.

If the roots of the equation $ax^2 + bx + c = 0$ are $l$ and $2l$,then:

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