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Roots of Quadratic Equation

If α and ...

Question

If $α$ and $β$ roots of ${a x}^{2} b x + c = 0$ , then evaluate $(α + 1) (β + 1)$

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Solution

$α + β = \frac{- b}{a}$

$α β = \frac{c}{a}$

$(α + 1) (β + 1)$

$= α β + α + β + 1$

$= \frac{c}{a} - \frac{b}{a} + 1$

$= \frac{c - b + a}{a}$

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