f(x)= 2x2-3x-2 Determine the zeros of each function by factoring:

The roots of f(x) =  2x^2-3x-2 are required.

Solve the quadratic equation 2x^2 - 3x - 2 = 0.

The roots of a quadratic equation ax^2 + bx + c = 0 are given by `(-b+-sqrt(b^2-4ac))/(2a)`

For the equation 2x^2 - 3x - 2 = 0, a = 2, b = -3 and c = -2, the roots of the equation are:

`(-(-3)+-sqrt((-3)^2-4*2*-2))/(2*2)`

`(3+-sqrt(9 + 16))/4`

`(3+-sqrt 25)/4`

`(3+- 5)/4`

8/4 and -2/4

2 and -1/2

The roots of f(x) =  2x^2-3x-2 are 2 and -1/2