# Polynomials : Algebraic Division and Complex Roots

The polynomial:

4x^4 - 6x^3 + 4x^2 - 3x + 1 has the real roots at x = 1 and x = 1/2 and two complex conjugate roots.

(a) by the process of algebraic division and then solving a quadratic equation, find the complex roots.

(b) Write down all the factors of the 4th degree polynomial

4x^4 - 6x^3 + 4x^2 - 3x + 1

(c) Find the gradient of the curve y = 4x^4 - 6x^3 + 4x^2 - 3x + 1 at the point where x=2.

(note - x is the letter x)