2018 · Q15
If α and β are the roots of the equation ax² + bx + c = 0, then what is the value of the expression (α + 1)(β + 1)?
Elementary MathematicsAlgebra
- A(a + b + c)/a
- B(b + c - a)/a
- C(a - b + c)/a
- D(a + b - c)/a
Explanation
Expand: (α + 1)(β + 1) = αβ + (α + β) + 1. Using αβ = c/a and α + β = −b/a gives c/a − b/a + 1 = (a − b + c)/a, option (C).