First slide

Theory of equations

Question

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

Moderate

A

$α - 1, β - 1$
B

$\frac{α + 1}{α}, \frac{1 + β}{β}$
C

$α + 1, β + 1$
D

$\frac{1 - α}{α}, \frac{1 - β}{β}$

Solution

$Roots of the equation c x^{2} + b x + a = 0 are α and β .$
$So, roots of the equation a x^{2} + b x + c = 0 are \frac{1}{α}, \frac{1}{β} .$
$Hence, roots of the equation a (x + 1)^{2} + b (x + 1) + c = 0 are:$
$\frac{1}{α} - 1 = \frac{1 - α}{α} and \frac{1}{β} - 1 = \frac{1 - β}{β}$

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