To find the zeros of the quadratic function f(x) = 8x² + 16x – 15, we need to solve the equation f(x) = 0.
This means we set up the equation:
8x² + 16x – 15 = 0
We can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
Here, a = 8, b = 16, and c = -15. First, we calculate the discriminant (the part under the square root):
b² – 4ac = (16)² – 4(8)(-15) = 256 + 480 = 736
Now, we can plug this back into the quadratic formula:
x = (-16 ± √736) / (2 * 8)
Calculating the square root of 736 gives us approximately 27.14. So:
x = (-16 ± 27.14) / 16
This results in two potential solutions:
1. x = (-16 + 27.14) / 16 ≈ 0.70
2. x = (-16 – 27.14) / 16 ≈ -2.68
Therefore, the zeros of the function f(x) = 8x² + 16x – 15 are approximately x ≈ 0.70 and x ≈ -2.68.