First slide

Theory of equations

Question

Let $α, β, γ$ be the roots of the equation $(x - a) (x - b) (x - c) = d, d \neq 0$ the roots of the equation $(x - α) (x - β) (x - γ) + d = 0$ are

Moderate

A

a, b, d
B

b, c, d
C

a, b, c
D

a + d, b + d, c + d

Solution

Since, $α, β, γ$ are the roots of $(x - a) (x - b) (x - c) = d$

$\begin{aligned} \Rightarrow (x - a) (x - b) (x - c) - d = (x - α) (x - β) (x - γ) \\ \Rightarrow (x - α) (x - β) (x - γ) + d = (x - a) (x - b) (x - c) \end{aligned}$
$\Rightarrow$ a, b and c are the roots of
$(x - α) (x - β) (x - γ) + d = 0$

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