If α , β , γ are the roots of the equation 4 x 3 + 12 x 2 - 7 x + 165 = 0 and α + 5 , β + 5 , γ + 5 are the roots of the equation a x 3 + b x 2 + c x + d = 0 then the product of the roots of the second equation is

Question

If α , β , γ are the roots of the equation 4 x 3 + 12 x 2 - 7 x + 165 = 0 and α + 5 , β + 5 , γ + 5 are the roots of the equation a x 3 + b x 2 + c x + d = 0 then the product of the roots of the second equation is, 27, 0, - 3, 3 5 + 4

MARKS App · Accepted Answer

It is given that α , β and γ are the roots at the equation 4 x 3 + 12 x 2 - 7 x + 165 = 0 , therefore α + β + γ = - 3 ⋯ i α β + β γ + γ α = - 7 4 ⋯ ii α β γ = - 165 4 ⋯ iii Now, required product is = α + 5 β + 5 γ + 5 = α β + 5 α + β + 25 γ + 5 = α β γ + 5 α β + β γ + γ α + 25 α + β + γ + 125 = - 165 4 + 5 - 7 4 + 25 - 3 + 125 = - 165 - 35 4 + 50 = - 200 4 + 50 = 0

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