If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$, then the quadratic equation whose roots are $\alpha$ and $\beta$ is

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Aicharya · Accepted Answer

Given that, $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$ $ \begin{array}{rlrl} \Rightarrow & & (\alpha+\beta)\left(\alpha^2+\beta^2-\alpha \betaight) & =-56 \ \Rightarrow & \alpha^2+\beta^2-\alpha \beta & =28 \end{array} $ $ \begin{aligned} 	ext { Now, } & & (\alpha+\beta)^2 & =(-2)^2 \ \Rightarrow & & \alpha^2+\beta^2+2 \alpha \beta & =4 \ \Rightarrow & & 28+3 \alpha \beta & =4 \ \Rightarrow & & \alpha \beta & =-8 \end{aligned} $ $	herefore$ Required equation is $ \begin{array}{rlrl} & & x^2-(-2) x+(-8) & =0 \ \Rightarrow & x^2+2 x-8 & =0 \end{array} $

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$, then the quadratic equation whose roots are $\alpha$ and…

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