2020 · Q12
If α and β are the roots of the quadratic equation x² + kx - 15 = 0 such that α - β = 8, then what is the positive value of k?
Elementary MathematicsAlgebra
- A2
- B3
- C4
- D5
Explanation
For x² + kx − 15 = 0, α + β = −k and αβ = −15. From (α − β)² = (α + β)² − 4αβ: 64 = k² + 60, so k² = 4. The positive value of k is 2.