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Algebra
Quadratic Equations, Sum and Product of Roots
jee_main_2026_april_8_shift_1
Grade None

Question:

If the quadratic equation x² - 12x + k = 0 has roots α and β such that α² + β² = 80, find k.

Step-by-Step Solution

Key Concept: Use α² + β² = (α+β)² - 2αβ.
Step 1: α + β = 12. Step 2: α² + β² = (α+β)² - 2αβ = 144 - 2k = 80 => 2k = 64 => k = 32.
Correct Answer: 32
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