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Algebra

Quadratic Equations, Symmetric Functions

jee_main_2026_april_8_shift_1

Grade None

Question:

If α and β are the roots of x² - 4x + 1 = 0, find the value of α³ + β³.

A. 52

B. 56

C. 60

D. 64

Step-by-Step Solution

Key Concept: α³ + β³ = (α+β)³ - 3αβ(α+β).

Step 1: α+β = 4, αβ = 1. Step 2: α³ + β³ = (α+β)³ - 3αβ(α+β) = 4³ - 3(1)(4) = 64 - 12 = 52.

Correct Answer: A

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