Final answer:
The zeros of the function f(x) = 2x³ - x² - 13x - 6 can be found by using the quadratic formula. Substituting the values into the formula, we get x = -3 and x = 1.5 as the zeros of the function.
Step-by-step explanation:
The zeros of the function f(x) = 2x³ - x² - 13x - 6 can be found by solving the equation f(x) = 0. To do this, we can use factoring or the quadratic formula. In this case, factoring may be difficult, so let's use the quadratic formula.
The quadratic formula states that for an equation of the form ax² + bx + c = 0, the zeros can be found using the formula:
x = (-b ± √(b² - 4ac)) / 2a
For our function f(x), a = 2, b = -1, and c = -6. Substituting these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)² - 4(2)(-6))) / (2(2))
Simplifying further, we have:
x = (1 ± √(1 + 48)) / 4
x = (1 ± √49) / 4
x = (1 ± 7) / 4
Therefore, the zeros of the function f(x) = 2x³ - x² - 13x - 6 are x = -3 and x = 1.5.