Question

ifα,β are zeroes of the polynomial x²-4x+7, find the quadratic polynomial whose zeroes are 2/α and 2/β

Answer 1

Any polynomial is given by x^2-sx+p=0, where s is sum of zeroes and p is product of zeroes.
Given zeroes are 2/a and 2/b. There sum is 2(a+b)/ab and their product is 2/ab. By using sum of zeroes is -b/a and product of zeroes is c/a, we get the required polynomial as x^2-8x/7 +2/7=0 or 7x^2-8x+2=0