Question

Determine the zeros for `g(x)=2x^2-x-6`?

Answer 1

`x=-3/2" "` or `" "x = 2`

Explanation:

Given:

`g(x) = 2x^2-x-6`

We can factor this quadratic using an AC method:

Find a pair of factors of `AC = 2*6 = 12` which differ by `B=1`

The pair `4, 3` works in that `4 * 3 = 12` and `4 - 3 = 1`.

Use this pair to split the middle term and factor by grouping:

`g(x) = 2x^2-x-6`

`color(white)(g(x)) = (2x^2-4x)+(3x-6)`

`color(white)(g(x)) = 2x(x-2)+3(x-2)`

`color(white)(g(x)) = (2x+3)(x-2)`

Hence we find that `g(x)` has zeros `x=-3/2` and `x=2`