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Sum and Product of Roots of a Quadratic Equation

If α and ...

Question

If $α$ and $β$ are the roots of the quadratic equation $x^{2} = 3 x$ then find $α^{2} + β^{2}$

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Solution

$x^{2} = 3 x$
$x^{2} - 3 x = 0$
$x (x - 3) = 0$
$\Rightarrow x = 0, 3$
$α = 0 β = 3$
$α^{2} + β^{2} = 0 + 9$
$= 9$

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Sum and Product of Roots of a Quadratic Equation

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