CA Foundation · Quantitative Aptitude · Equations
If α and β are the roots of 2x² − 9x + 4 = 0, what is the value of α² + β²?
The value is 65/4. With α + β = 9/2 and αβ = 4/2 = 2, α² + β² = (α + β)² − 2αβ = 81/4 − 4 = 65/4. Using the identity avoids finding the roots individually.
- A49/4Correct
- B65/4
- C81/4
- D73/4
Explanation
α + β = 9/2 and αβ = 2. α² + β² = (α+β)² − 2αβ = 81/4 − 4 = 65/4. Check: 81/4 − 16/4 = 65/4. So the correct value is 65/4, not 49/4.
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