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Algebra

Quadratic Equations, Sum and Product of Roots

jee_main_2026_jan_22_shift_1

Grade None

Question:

If the quadratic equation \(x^2 - 10x + k = 0\) has roots \(\alpha\) and \(\beta\) such that \(\alpha^2 + \beta^2 = 58\), 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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