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Roots of Quadratic Equation

If α and ...

Question

If $α$ and $β$ are the roots of $x^{2} + 5 x - = 0$ then find
(i) $α^{3} + β^{3}$
(ii) $α^{2} + β^{2}$ .

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Solution

$x^{2} + 5 x - = 0$

$x^{2} + 5 x = 0$

$x (x + 5) = 0$

$x = 0, - 5$

$∴ α = 0, β = - 5$

$α^{3} + β^{3}$

$= 0^{3} + (- 5)^{3}$

$= - 125$

$α^{2} + β^{2}$

$= 0^{2} + (- 5)^{2}$

$= 25$

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