Question

If alpha and beta are zeros of p(x)=x²+ax+b, then find a polynomial whose zeros are 1÷alpha and 1÷beta.

Answer 1

? and ? are the roots of x2 + px + q. Therefore,? + ? = -p and ?? = q Now, 1/? + 1/? = ?+?/?? = -p/q1/? . 1/? = 1/?? = 1/q Thus, the required polynomial is:x2 - (sum of roots)x + (product of roots)x2 - (-p/q)x + 1/q or qx2 + px + 1