CMA Foundation · Fundamentals of Business Mathematics and Statistics · Quadratic Equations
If α and β are the roots of 3x² − 6x + 2 = 0, what is the value of α² + β²?
The value of α² + β² is 8/3. The sum of roots is 2 and the product is 2/3. Using the identity (α+β)² − 2αβ gives 4 − 4/3 = 8/3. Subtracting only one times the product would wrongly give 10/3.
- A8/3Correct
- B4
- C2
- D10/3
Explanation
Sum α+β = 6/3 = 2 and product αβ = 2/3. Then α² + β² = (α+β)² − 2αβ = 4 − 4/3 = 8/3. Forgetting to double the product gives 4 − 2/3 = 10/3, which is wrong.
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