Question

Write a quadratic polynomial whose sum of zeroes is 1/4 and product of zeroes is −1.

Find a quadratic polynomial the sum and product of whose zeroes are √2 and −3/2 respectively.

If α and β are the zeroes of the quadratic polynomial x² − 4x + 3, form a quadratic polynomial whose zeroes are 2α and 2β.

If α and β are the zeroes of the polynomial p(x) = 2x² − 5x + 7, find a polynomial whose zeroes are 2α + 3β and 3α + 2β.