Algebra
Quadratic Equations, Sum and Product of Roots
jee_main_2026_april_4_shift_2
Grade 12
Question:
If the quadratic equation x^2 - 5x + k = 0 has roots α and β such that α + β = 5 and α^2 + β^2 = 13, find the value of k.
Step-by-Step Solution
Key Concept: Use α^2 + β^2 = (α+β)^2 - 2αβ.
Step 1: α + β = 5. Step 2: α^2 + β^2 = (α+β)^2 - 2αβ = 25 - 2αβ = 13 => 2αβ = 12 => αβ = 6. Step 3: k = αβ = 6.
Correct Answer: 6
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