Question

What are the zeros of the function h(x) = 2x² + x - 15?

a) x = -3 and x = -5/2
b) x = -3 and x = 5/2
c) x = -5/2 and x = 3
d) x = 5/2 and x = 3

Answer 1

The zeros of the quadratic function h(x) = 2x² + x - 15 are found using the quadratic formula, resulting in x = -3 and x = 5/2 as the solutions, which corresponds to option b).

Step-by-step explanation:

The zeros of a function can be found by setting the function equal to zero and solving for the variable. In this case, the function h(x) = 2x² + x - 15 can be rewritten as 2x² + x - 15 = 0 and solved using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation in the form ax² + bx + c = 0.

Substituting the values a = 2, b = 1, and c = -15 into the formula, we would get two solutions for x, which are the zeros of the function. The correct zeros of the function h(x) = 2x² + x - 15 are x = -3 and x = 5/2 or x = 2.5. Therefore, the correct answer is option b): x = -3 and x = 5/2.