Single correct option
If α and β are the roots of x² − px + q = 0 such that α + β = 10 and α² + β² = 58, what is the value of q?
- A. 21
- B. 24
- C. 29
- D. 42
Show answer and solution
Answer: (A) 21
α² + β² = (α + β)² − 2αβ, so 58 = 100 − 2αβ, giving αβ = 21.
For x² − px + q = 0, the product of the roots is q, so q = 21.
(The roots are 3 and 7: 9 + 49 = 58 ✓.) 42 is 2αβ — a slip if you forget to halve.
For x² − px + q = 0, the product of the roots is q, so q = 21.
(The roots are 3 and 7: 9 + 49 = 58 ✓.) 42 is 2αβ — a slip if you forget to halve.
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