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

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(B) Given the quadratic equation $x^2 - 4x + 1 = 0$.Comparing with $ax^2 + bx + c = 0$,we have $a=1, b=-4, c=1$.Sum of roots: $\alpha + \beta = -b/a =

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$52$

Vedclass · Answer

(B) Given the quadratic equation $x^2 - 4x + 1 = 0$.Comparing with $ax^2 + bx + c = 0$,we have $a=1, b=-4, c=1$.Sum of roots: $\alpha + \beta = -b/a = -(-4)/1 = 4$.Product of roots: $\alpha \beta = c/a = 1/1 = 1$.We know the identity: $\alpha^3 + \beta^3 = (\alpha + \beta)^3 - 3\alpha \beta (\alpha + \beta)$.Substituting 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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