If = 4 and 3 + 3 = 44, then are the roots of the equation

Question

If $α + β = 4$ and $α^{3} + β^{3} = 44$ , then $α, β$ are the roots of the equation

Smart Achievers · Accepted Answer

(1)

$α + β = 4,$ $α^{3} + β^{3} = 44$

Taking, ${(α + β)}^{3} = α^{3} + β^{3} + 3 α β (α + β)$

${(4)}^{3} = 44 + 3 α β (4)$ $\Rightarrow 64 - 44 = 12 α β$

$\Rightarrow 12 α β = 20 \Rightarrow α β = \frac{20}{12} = \frac{5}{3}$

So, equation will be $x^{2} - 4 x + p = 0$

$x^{2} - 4 x + \frac{5}{3} = 0$ or $3 x^{2} - 12 x + 5 = 0$

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