CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
If α and β are the roots of 3x² − 5x − 2 = 0, what is the value of α² + β²?
The value is 37/9. The sum of roots is 5/3 and the product is −2/3, so α² + β² = (5/3)² − 2(−2/3) = 25/9 + 12/9 = 37/9. The actual roots 2 and −1/3 give 4 + 1/9, which matches.
- A37/9Correct
- B25/9
- C13/9
- D31/9
Explanation
α+β = 5/3 and αβ = −2/3. α²+β² = (α+β)² − 2αβ = 25/9 + 4/3 = 25/9 + 12/9 = 37/9. Check with actual roots 2 and −1/3: 4 + 1/9 = 37/9. Using +2αβ would wrongly give 13/9.
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