Final answer:
To find the zeros of the function f(x) = 2x² + 14.4x + 21.4, use the quadratic formula to solve for x. The zeros are approximately x = -4.218 and x = -1.182.
Step-by-step explanation:
To find the zeros of the function f(x) = 2x² + 14.4x + 21.4, we need to set the function equal to zero and solve for x. 2x² + 14.4x + 21.4 = 0. We can use the quadratic formula, x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
In this case, a = 2, b = 14.4, and c = 21.4. Substituting these values into the quadratic formula, we get x = (-14.4 ± √(14.4² - 4(2)(21.4))) / (2(2)). Simplifying further, we have x = (-14.4 ± √(207.36 - 171.2)) / 4. Evaluating the square root and simplifying, we get x = (-14.4 ± √36.16) / 4. Taking the square root gives us x = (-14.4 ± 6.016) / 4.
Rounded to the nearest hundredth, the zeros of the function f(x) = 2x² + 14.4x + 21.4 are approximately x = -4.218 and x = -1.182.
Learn more about Finding zeros of a quadratic function