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Algebra

Quadratic Equations, Sum and Product of Roots

jee_main_2026_april_6_shift_2

Grade None

Question:

If the quadratic equation x² - 10x + k = 0 has roots α and β such that α² + β² = 58, find k.

Step-by-Step Solution

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

Step 1: α + β = 10. Step 2: α² + β² = (α+β)² - 2αβ = 100 - 2k = 58 => 2k = 42 => k = 21.

Correct Answer: 21

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