CA Foundation · Quantitative Aptitude · Equations
If α and β are the roots of x² − 6x + 4 = 0, what is the value of α² + β²?
The value of α² + β² is 28. With sum of roots 6 and product 4, use the identity (α + β)² − 2αβ, which gives 36 minus 8, equal to 28. Forgetting the factor 2 would give 32, which is wrong.
- A36
- B32Correct
- C28
- D20
Explanation
α + β = 6 and αβ = 4. α² + β² = (α + β)² − 2αβ = 36 − 8 = 28. Wait: 36 − 8 = 28, so the correct value is 28. Option 32 would come from 36 − 4, using αβ instead of 2αβ.
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