Final answer:
To find the zeros of the function algebraically, we can use the quadratic formula. By substituting the values into the formula and simplifying, we find that the zeros of the function are 2/3 and -2.
Step-by-step explanation:
To find the zeros of the function algebraically, we need to solve the equation f(x) = 3x² + 4x - 4 = 0. We can use the quadratic formula to solve this equation. The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / 2a
For our equation, a = 3, b = 4, and c = -4. Substituting these values into the quadratic formula, we get:
x = (-4 ± √(4² - 4(3)(-4))) / 2(3)
Simplifying further, we have:
x = (-4 ± √(16 + 48)) / 6
x = (-4 ± √64) / 6
x = (-4 ± 8) / 6
Therefore, the zeros of the function are:
x = (-4 + 8) / 6 = 4/6 = 2/3
x = (-4 - 8) / 6 = -12/6 = -2
Learn more about Finding zeros of a quadratic function