How do you find the rest of the zeros given one of the zero c=1/2 and the function f(x)=2x^3-3x^2-11x+6?

Feb 15, 2017

-2 and 3

Explanation:

$c = \frac{1}{2}$ being a zero of the polynomial, $x - \frac{1}{2}$ would be a factor.

Now divide the polynomial by $\left(x - \frac{1}{2}\right)$ as shown below using synthetic division

Quotient is now $2 {x}^{2} - 2 x - 12$

or, $2 \left({x}^{2} - x - 6\right)$ Now factorise this quadratic expression

$2 \left(x - 3\right) \left(x + 2\right)$

The rest of the zeros are therefor x= -2 and x=3