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(B) For the quadratic equation $x^2 - 4x + 1 = 0$,the sum of the roots is $\alpha + \beta = -(-4)/1 = 4$ and the product of the roots is $\alpha \beta

Vedclass · Accepted Answer

$52$

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(B) For the quadratic equation $x^2 - 4x + 1 = 0$,the sum of the roots is $\alpha + \beta = -(-4)/1 = 4$ and the product of the roots is $\alpha \beta = 1/1 = 1$.Using the algebraic identity $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha \beta (\alpha + \beta)$,Substitute the values: $\alpha^3 + \beta^3 = (4)^3 - 3(1)(4)$.$\alpha^3 + \beta^3 = 64 - 12 = 52$.

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 1 = 0$,the value of $\alpha^3 + \beta^3$ is

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