Algebra
Quadratic Equations, Symmetric Functions
jee_main_2026_april_6_shift_2
Grade None
Question:
If α and β are the roots of 2x² - 5x + 2 = 0, find the value of α/β + β/α.
A. 15/4
B. 17/4
C. 19/4
D. 21/4
Step-by-Step Solution
Key Concept: α/β + β/α = (α² + β²)/(αβ) = [(α+β)² - 2αβ]/(αβ).
Step 1: For 2x² - 5x + 2 = 0, α+β = 5/2, αβ = 2/2 = 1. Step 2: α/β + β/α = (α² + β²)/(αβ) = [(α+β)² - 2αβ]/(αβ). Step 3: = [(5/2)² - 2(1)]/1 = (25/4 - 2) = (25/4 - 8/4) = 17/4.
Correct Answer: B
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