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Algebra

Quadratic Equations, Sum and Product of Roots

jee_main_2026_april_5_shift_1

Grade 12

Question:

If the quadratic equation x² - 8x + k = 0 has roots α and β such that α² + β² = 34, find k.

Step-by-Step Solution

Key Concept: Use α² + β² = (α+β)² - 2αβ.

Step 1: α + β = 8. Step 2: α² + β² = (α+β)² - 2αβ = 64 - 2k = 34 => 2k = 30 => k = 15.

Correct Answer: 15

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