P(x)=2x^4+3x^3-8x^2-9x+6

Question

Find all real zeros of the polynomial

Answer 1

The easiest way to solve this is to graph it first, but if that is not allowed use the rational roots theorem

to show that -2 is a root. (Use synthetic division)

Divide that out to get 2x³-x²-6x+3.

Proceed as before to show that 1/2 is a root and divide it out.

Then you have 2x²-6 which has roots ±√3.