Find a quadratic polynomial
Q1. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4, −1
Q2. If α and β are the zeroes of the polynomial f(x)=x2−2x−3, find the polynomial whose zeroes are 2α−1 and 2β−1.
Q3. If α,β are the zeroes of polynomial f(x)=x2−p(x+1)−c, then (α+1)(β+1)=
Q4. If α and β are the zeroes of polynomial f(x)=x2−p(x+1)+c such that (α+1)(β+1)=0, then find the value of c.
Q5. If α and β are the roots of x2−x+2=0, then find α3β+αβ3