CA Foundation · Quantitative Aptitude · Equations
The roots of the equation x² − 7x + 12 = 0 are α and β. What is the value of α² + β²?
The value is 25. Using the identity α² + β² = (α + β)² − 2αβ with sum 7 and product 12 gives 49 − 24 = 25. This agrees with the actual roots 3 and 4, whose squares are 9 and 16.
- A25Correct
- B49
- C1
- D37
Explanation
α + β = 7 and αβ = 12. α² + β² = (α + β)² − 2αβ = 49 − 24 = 25. Check: roots are 3 and 4, and 9 + 16 = 25. Option 37 results from adding 2αβ instead of subtracting it.
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