If α , β , γ are the roots of the equation x 3 − 3 x 2 + 2 x − 1 = 0 , then the value of ( 1 − α ) ( 1 − β ) ( 1 − γ ) is

Question

If α , β , γ are the roots of the equation x 3 − 3 x 2 + 2 x − 1 = 0 , then the value of ( 1 − α ) ( 1 − β ) ( 1 − γ ) is, 1, 2, − 1, − 2

MARKS App · Accepted Answer

We have, x 3 − 3 x 2 + 2 x − 1 So, α + β + γ = 3 α β + β γ + γ α = 2 α β γ = 1 Now, ( 1 − α ) ( 1 − β ) ( 1 − γ ) = 1 − ( α + β + γ ) + ( α β + β γ + γ α ) − α β γ = 1 − 3 + 2 − 1 = − 1

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