Algebra
Polynomial Equations, Roots and Factors
jee_adv_2026_mock_p2
Grade 12
Question:
If the roots of the equation x^3 - 6x^2 + 11x - 6 = 0 are α, β, γ, find the value of (α-2)(β-2)(γ-2).
Step-by-Step Solution
Key Concept: Factor the polynomial directly.
Step 1: x^3 - 6x^2 + 11x - 6 = (x-1)(x-2)(x-3). Step 2: Roots are 1, 2, 3. Step 3: (α-2)(β-2)(γ-2) = (1-2)(2-2)(3-2) = (-1)(0)(1) = 0.
Correct Answer: 0
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