Question

If alpha and beta are zeroes of quadratic polynomial f(x)= x^2- 2x+3, find a polynomial whose roots are (I) alpha+2,beta+2
(ii) alpha-1/alpha+1, beta-1/beta+1

Answer 1

F(x)=x^2-2x+3
Alpha+beta=-b/a=2
Alpha×beta=c/a=3
i)sum:
Alpha+2+beta+2
=alpha+beta+4
=2+4=6
Product:
(Alpha+2)(beta+2)
=alpha×beta+2alpha+2beta+4
=3+2(2)+4
=7+4=11