Let α, β, γ be the roots of the equation (x-a)(x-b)(x-c)=d,(d ≠ 0), then the roots of the equation (x-α)(x-β)(x-γ)+d=0, is

Question

Let α, β, &gamma; be the roots of the equation (x-a)(x-b)(x-c)=d,(d ≠ 0), then the roots of the equation (x-α)(x-β)(x-&gamma;)+d=0, is (A) a + d , b + d , c + d (B) a, b, c (C) b c.d (D) a b, d

Tardigrade Admin · Accepted Answer

( x - a )( x - b )( x - c )- d =( x -α)( x -β)( x -&gamma;) ⇒( x -α)( x -β)( x -&gamma;)+ d =( x - a )( x - b )( x - c ) ⇒ a , b , c

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

$a + d, b + d, c + d$

$a, b, c$

$b c . d$

$ab, d$

$(x - a) (x - b) (x - c) - d = (x - α) (x - β) (x - γ)$
$\Rightarrow (x - α) (x - β) (x - γ) + d = (x - a) (x - b) (x - c)$
$\Rightarrow a, b, c$

Q. Let α,β,γ be the roots of the equation (x−a)(x−b)(x−c)=d,(d=0), then the roots of the equation (x−α)(x−β)(x−γ)+d=0, is

a+d,b+d,c+d

a,b,c

bc.d

ab,d