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CAT 2025 Slot 1 · Quant · Quadratic Equations and Polynomials · medium

If α and β are the roots of x² − 7x + 12 = 0, what is the value of α² + β²?

Single correct option

If α and β are the roots of x² − 7x + 12 = 0, what is the value of α² + β²?
  1. A. 13
  2. B. 19
  3. C. 25
  4. D. 37
Show answer and solution

Answer: (C) 25

Sum of roots α+β = 7, product αβ = 12 (by Vieta's formulas, comparing with x²−(sum)x+(product)). α²+β² = (α+β)² − 2αβ = 49 − 24 = 25. (Check: roots are actually 3 and 4, and 3²+4² = 9+16 = 25.)
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Original question written in the CAT 2025 Slot 1 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake