2021 · Q18
If p and q (p > q) are the roots of the equation x² − 60x + 899 = 0, then which one of the following is correct ?
Elementary MathematicsAlgebra
- Ap − q − 1 = 0
- Bp − 2q + 27 = 0
- C2p − q − 30 = 0
- D3p − 2q − 43 = 0
Explanation
The discriminant is 60² − 4·899 = 3600 − 3596 = 4, so the roots are (60 ± 2)/2 = 31 and 29. Thus p = 31, q = 29. Checking option (b): p − 2q + 27 = 31 − 58 + 27 = 0. None of the other options vanish, so the answer is option (b).