2016 · Q13
If the linear factors of ax²-(a² +1 )x + a are p and q, then p + q is equal to
Elementary MathematicsAlgebra
- A(x - 1)(a + 1)
- B(x + 1)(a+1)
- C(x - 1)(a- 1)
- D(x + 1)(a- 1)
Explanation
Factorising: ax²−(a²+1)x+a = ax(x−a)−(x−a) = (x−a)(ax−1). Thus the linear factors are p = x−a and q = ax−1 (in some order). Their sum is p+q = x−a+ax−1 = (x−1)(a+1), option A.