Example - Finding roots of a cubic polynomial
Find the roots of \({x^3} + 4{x^2} + x - 6 = 0\)
Solution
First, we need to find which number when substituted into the equation will give the answer zero.
\(f(1) = {(1)^3} + 4{(1)^2} + (1) - 6 = 0\)
Therefore \((x - 1)\)is a factor.
Factorise the quadratic until the expression is factorised fully.
\((x - 1)({x^2} + 5x + 6) = 0\)
\((x - 1)(x + 3)(x + 2) = 0\)
\(x - 1 = 0\,so\,x = 1\)
\(x + 3 = 0\,so\,x = - 3\)
\(x + 2 = 0\,so\,x = - 2\)
Therefore the roots occur when \(x\) = -3, -2 and 1.
