Question
Find the smallest zero for the function h(x)=4x^2-8x-60
Answers
GPT 3.5
To find the zeros of the function h(x) = 4x^2 - 8x - 60, we need to solve the quadratic equation h(x) = 4x^2 - 8x - 60 = 0.
We can solve this quadratic equation using the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4(4)(-60))) / (2 * 4)
x = (8 ± √(64 + 960)) / 8
x = (8 ± √1024) / 8
x = (8 ± 32) / 8
This gives us two possible solutions for x:
1. x = (8 + 32) / 8 = 40 / 8 = 5
2. x = (8 - 32) / 8 = -24 / 8 = -3
Therefore, the smallest zero for the function h(x) = 4x^2 - 8x - 60 is x = -3.
We can solve this quadratic equation using the quadratic formula:
x = (-(-8) ± √((-8)^2 - 4(4)(-60))) / (2 * 4)
x = (8 ± √(64 + 960)) / 8
x = (8 ± √1024) / 8
x = (8 ± 32) / 8
This gives us two possible solutions for x:
1. x = (8 + 32) / 8 = 40 / 8 = 5
2. x = (8 - 32) / 8 = -24 / 8 = -3
Therefore, the smallest zero for the function h(x) = 4x^2 - 8x - 60 is x = -3.