First slide

Theory of equations

Question

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

Moderate

A

$b$
B

$- b$
C

$1 - b$
D

$b - 1$

Solution

Given equation $x^{2} - a (x + 1) - b = 0$
$\Rightarrow x^{2} - ax - a - b = 0 \Rightarrow α + β = a, αβ = - (a + b)$
Now $(α + 1) (β + 1) = αβ + α + β + 1$
$= - (a + b) + a + 1 = 1 - b$

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