Algebra
Quadratic Equations, Sum and Product of Roots
jee_main_2026_jan_21_shift_1
Grade None
Question:
If the equation x² - 5x + k = 0 has roots α and β such that α/β = 2/3, find the value of k.
Step-by-Step Solution
Key Concept: Use α + β = 5, αβ = k, and α/β = 2/3.
Step 1: α/β = 2/3 => α = 2t, β = 3t. Step 2: α+β = 5t = 5 => t = 1. Step 3: α = 2, β = 3. Step 4: k = αβ = 6.
Correct Answer: B
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