Question

If aplha and beta are the zeroes of the quadratic polynomial f (x) = 3x^2 -5x-2 then evalute alpha^2/beta + beta^2/alpha

Answer 1

first find out the zeroes of the equation

3x^2-5x-2

3x^2+x-6x-2 (split factorization )

x(3x+1)-2(3x+1)

(3x+1) (x-2)

x=-1/3 x=2

this are the zeroes now substitute each in alpha and beta

x=-1/3=alpha

x=2=beta

evaluate

(-1/3)^2/2+(2)^2/(-1/3)

=-215/18