Find the zeros of the function f(x)=−1.8x^2 +17x−37.7.
Round values to the nearest hundredth (if necessary).
To find the zeros of the function, we set f(x) equal to zero and solve for x.
Setting -1.8x^2 + 17x - 37.7 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = -1.8, b = 17, and c = -37.7. Plugging these values into the quadratic formula, we get:
x = (-17 ± √(17^2 - 4(-1.8)(-37.7))) / 2(-1.8)
Simplifying further:
x = (-17 ± √(289 - 271.44)) / -3.6
x = (-17 ± √17.56) / -3.6
Taking the square root:
x ≈ (-17 ± 4.19) / -3.6
Simplifying:
x ≈ (-17 + 4.19) / -3.6 ≈ -3.66
x ≈ (-17 - 4.19) / -3.6 ≈ 5.01
Rounding to the nearest hundredth, the zeros of the function are approximately:
x = -3.66 and x = 5.01