Question

If the alpha and beta are the zeroes of the polynomial x^2+px+q find the value of alpha/beta+2* beta/alpha+2

Answer 1

alpha =-b/a

=-p/1

beta=c/a

=q\1

(alpha/beta+2)(beta/alpha+2)

=(-p+q+2)(q-p+2)

=(q-p+2)(q-p+2)

=q^2-qp +2q-qp+p^2-2p+2q-2p+4

=q^2+p^2-2qp+4q-4p+4

=(q-p)^2+4(q-p)+4

--------------------Is the polynomial