Final answer:
To find the zeros of the function f(x)=0.7x^2-6x+6, apply the quadratic formula with coefficients a = 0.7, b = -6, and c = 6. This will yield two solutions for x, which, when calculated and rounded to the nearest hundredth, are approximately x ≈ 5.77 or x ≈ 1.57.
Step-by-step explanation:
To find the zeros of the function f(x)=0.7x^2-6x+6, you can use the quadratic formula:
x = √[(-b) +/- √(b^2-4ac)]/(2a)
First, identify the coefficients a = 0.7, b = -6, and c = 6. Plug these values into the quadratic formula:
x = √[(-(-6)) +/- √((-6)^2-4(0.7)(6))]/(2*0.7)
Calculating the discriminant (b^2 - 4ac):
√(36 - 16.8) = √(19.2)
Then, evaluate for both the + and - signs in the numerator:
x = (6 +/- √19.2) / 1.4
The final step is to calculate the two possible values for x, rounding to the nearest hundredth:
x ≈ 5.77 or x ≈ 1.57