2016 · Q10
Let p and q be non-zero integers. Consider the polynomial A(x)=x²+px+q It is given that (x - m) and (x - km) are simple factors of A(x), where m is a non-zero integer and k is a positive integer,k ≥ 2. Which one of the following is correct?
Elementary MathematicsAlgebra
- A(k+1)² p² = k q
- B(k+1)² q = k p²
- Ck² q = (k+1) p²
- Dk² p² = (k+1) q
Explanation
The factors (x−m) and (x−km) give roots m and km of x²+px+q. Hence m+km = −p and m·km = q, i.e. m(1+k) = −p and km² = q. Eliminating m gives k·p²/(1+k)² = q, i.e. (k+1)²q = kp², option B.