Let alpha and beta be the roots of the quadra | vedclass

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(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$.Dividing by $a$,we get $\frac{2b}{a} = 1 + \frac{c}{a}$ ... $(i)$.From the properties of r

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$-31$

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(C) Given that $a, b, c$ are in $A.P.$,we have $2b = a + c$.Dividing by $a$,we get $\frac{2b}{a} = 1 + \frac{c}{a}$ ... $(i)$.From the properties of roots,$\alpha + \beta = -\frac{b}{a} = 15$,which implies $\frac{b}{a} = -15$.Substituting $\frac{b}{a} = -15$ into equation $(i)$:$2(-15) = 1 + \frac{c}{a} \Rightarrow -30 = 1 + \frac{c}{a} \Rightarrow \frac{c}{a} = -31$.Since $\alpha\beta = \frac{c}{a}$,we have $\alpha\beta = -31$.

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $ax^2 + bx + c = 0$. If $a, b, c$ are in $A.P.$ and $\alpha + \beta = 15$,then $\alpha\beta$ equals:

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