Question

Does the quadratic function

f(x) = 4x2 + 5x – 29 have one,
two, or no real zeros? Utilize the
quadratic formula to determine
the answer.

Answer 1

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.