Question

Find all the zeroes of g(x)=4x^4+4x^3-11x^2-12x-3

Answer 1

The zeroes of
`g(x)=4x^4+4x^3-11x^2-12x-3` are
`-√(3), -(1)/(2), √(3)`, or approximately
`-1.732, -0.500, 1.732`.

Explanation:

Graphical calculator way (probably intended)

By inputting the function in a graphical calculator we can see that the roots of the graph of
`g` are about
`x=-1.732, x = 0.500, x = 1.732` (make sure you click on the points of interests).

Algebraic way (probably not intended because of obscure factoring)

Notice that
`g(x) = 4x^4+4x^3-11x^2-12x-3 = (2x-1)^2(x^2-3).` So the roots can be calculated with
`(2x-1)^2 = 0 \vee x^2 - 3 = 0`, yielding
`x = -(1)/(2) \vee x = \pm√(3)`.