2016 · Q31
Under what condition on p and q, one of the roots of the equation x²+x+q=0 is the square of the other?
Elementary MathematicsAlgebra
- A1 + q + q² = 3pq
- B1 + p + p² = 3pq
- Cp³ + q + q² = 3pq
- Dq³ + p + p² = 3pq
Explanation
Let the roots be α and α²: then α+α² = −p and α³ = q. Note that (α+α²)³ = α³(1+α)³. Substituting gives −p³ = q(1−3p+q), which rearranges to p³+q+q² = 3pq, option C.