If alpha and beta are the roots of the equati | vedclass

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(C) Given: $\alpha$ and $\beta$ are roots of the equation $ax^2+bx+c=0$. Sum of roots: $\alpha+\beta = -\frac{b}{a}$. Product of roots: $\alpha\beta =

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$acx^2+(ab+bc)x+b^2=0$

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(C) Given: $\alpha$ and $\beta$ are roots of the equation $ax^2+bx+c=0$. Sum of roots: $\alpha+\beta = -\frac{b}{a}$. Product of roots: $\alpha\beta = \frac{c}{a}$. New roots are $S_1 = \alpha+\beta = -\frac{b}{a}$ and $S_2 = \frac{1}{\alpha}+\frac{1}{\beta} = \frac{\alpha+\beta}{\alpha\beta} = \frac{-b/a}{c/a} = -\frac{b}{c}$. The required equation is $(x-S_1)(x-S_2) = 0$. $(x - (-\frac{b}{a}))(x - (-\frac{b}{c})) = 0$. $(x + \frac{b}{a})(x + \frac{b}{c}) = 0$. Multiplying by $ac$: $(ax+b)(cx+b) = 0$. $acx^2 + abx + bcx + b^2 = 0$. $acx^2 + (ab+bc)x + b^2 = 0$.

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is

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