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Inequalities Involving Modulus Function

If αand β ...

Question

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

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Solution

Consider the given equation.
${a x}^{2} - b x + c = 0$
$α + β = \frac{b}{a}$ $α β = \frac{c}{a}$
$(α + 1) (β + 1) = α β + β + α + 1$
$= \frac{c}{a} + \frac{b}{a} + 1 = \frac{a + b + c}{a}$

Hence, this is the answer.

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