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Roots of a Quadratic Equation

If α, β are t...

Question

If $α, β$ are the roots of the equation $x^{2} - 5 x + 6 = 0$ , then the value of $α^{3} + β^{3}$ is

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Solution

$x^{2} - 5 x + 6 = 0 \Rightarrow (x - 2) (x - 3) = 0 \Rightarrow x = 2, 3$
Now,
$α^{3} + β^{3} = 2^{3} + 3^{3} = 35$

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Roots of a Quadratic Equation

Standard XII Mathematics

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