Final answer:
The quadratic function f(x) = 4x² + 5x − 29 has two real zeros, as indicated by the positive discriminant when using the quadratic formula.
Step-by-step explanation:
To determine the number of real zeros a quadratic function has, we can utilize the quadratic formula. For a quadratic function of the form ax²+bx+c = 0, the quadratic formula is:
x = (-b ± √(b² - 4ac)) / (2a)
In the case of the quadratic function f(x) = 4x² + 5x − 29, we identify a = 4, b = 5, and c = -29. Plugging these values into the discriminant portion b² - 4ac of the quadratic formula:
Discriminant = 5² - 4(4)(-29) = 25 + 464 = 489
Since the discriminant is a positive number, the quadratic equation has two real zeros, as the square root of a positive number is real.
Therefore, using the quadratic formula, we can find the exact values of these zeros.