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

Question

Dr. Abubacker · Accepted Answer

(d)
Given that, $\alpha + \beta = - 2$ and $\alpha^{3} + \beta^{3} = - 56$
$\Rightarrow (\alpha + \beta)\left( \alpha^{2} + \beta^{2} - \alpha\beta ight) = - 56$
$\Rightarrow \ \alpha^{2} + \beta^{2} - \alpha\beta = 28$
Also, $(\alpha + \beta)^{2} = ( - 2)^{2}$
$\Rightarrow \ \alpha^{2} + \beta^{2} + 2\alpha\beta = 4$
$\Rightarrow 28 + 3\alpha\beta = 4$
$\Rightarrow \ \alpha\beta = - 8$
$	herefore$ Required equation is $x^{2} + 2x - 8 = 0$

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

Explanation

Reviewed by Dr. Abubacker

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