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Algebra of Limits

If α and ...

Question

If $α$ and $β$ are the roots of the equation $3 x^{2} - 6 x + 4 = 0$ , find the value of $α^{2} + β^{2}$ ?

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Solution

Given, $α, β$ are the roots of $3 x^{2} - 6 x + 4 = 0$
Therefore, $α + β = \frac{- b}{a} = \frac{- (- 6)}{3} = \frac{6}{3} = 2$
and $α β = \frac{c}{a} = \frac{4}{3}$
We know, $α^{2} + β^{2} = (α + β)^{2} - 2 α β$
$= 2^{2} - 2 (\frac{4}{3}) = 4 - \frac{8}{3}$
$= \frac{12 - 8}{3}$
$= \frac{4}{3}$

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