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(C) Given that $\alpha$ and $\beta$ are the roots of $x^2 + bx - c = 0$.From the properties of roots,we have:Sum of roots: $\alpha + \beta = -b \impli

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$x^2 + [(\alpha + \beta) + \alpha \beta]x + \alpha \beta(\alpha + \beta) = 0$

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(C) Given that $\alpha$ and $\beta$ are the roots of $x^2 + bx - c = 0$.From the properties of roots,we have:Sum of roots: $\alpha + \beta = -b \implies b = -(\alpha + \beta)$Product of roots: $\alpha \beta = -c \implies c = -\alpha \beta$We need to find the equation whose roots are $b$ and $c$.Sum of new roots: $b + c = -(\alpha + \beta) - \alpha \beta = -[(\alpha + \beta) + \alpha \beta]$Product of new roots: $bc = [ -(\alpha + \beta) ] 	imes [ -\alpha \beta ] = (\alpha + \beta)(\alpha \beta)$The required quadratic equation is given by $x^2 - (	ext{sum of roots})x + (	ext{product of roots}) = 0$.Substituting the values: $x^2 - (-[(\alpha + \beta) + \alpha \beta])x + (\alpha + \beta)(\alpha \beta) = 0$$x^2 + [(\alpha + \beta) + \alpha \beta]x + \alpha \beta(\alpha + \beta) = 0$.

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2 + bx - c = 0$,then the equation whose roots are $b$ and $c$ is

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