Question

7. Describe the number and type of roots for the polynomial (how many real and complex?)

x^3 + 5x^2 - 4x - 2= 0

Answer 1

sketch graph

at x = -oo it goes to -oo

at x = -1 it is +6

at x = 0 it is-2

at x = +oo it is +oo
SO
it crosses the x axis three times, three real roots

Answer 2

x^3 + 5x^2 - 4x - 2
= (x-1)(x^2+6x+2)

The discriminant of the quadratic is positive, so it has two real roots.