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Algebra

Quadratic Equations, Symmetric Functions

jee_main_2026_april_5_shift_1

Grade 12

Question:

Let α and β be the roots of x² - 3x + 1 = 0. Find the value of α⁴ + β⁴.

A. 7

B. 12

C. 47

D. 54

Step-by-Step Solution

Key Concept: Use α+β = 3, αβ = 1. Then α²+β² = (α+β)² - 2αβ, and α⁴+β⁴ = (α²+β²)² - 2(αβ)².

Step 1: α+β = 3, αβ = 1. Step 2: α²+β² = (α+β)² - 2αβ = 9 - 2 = 7. Step 3: α⁴+β⁴ = (α²+β²)² - 2(αβ)² = 49 - 2 = 47.

Correct Answer: C

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