To find the zeros of the quadratic function, we need to solve the equation f(x) = 0. This involves using the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this case, the coefficients are:
- a = 9
- b = 54
- c = 19
First, we compute the discriminant:
b² – 4ac = 54² – 4(9)(19)
= 2916 – 684 = 2232
Since the discriminant is positive, there are two distinct real zeros. Now, let’s calculate the values:
x = (-54 ± √2232) / (2 * 9)
√2232 ≈ 47.23
Now plug this back into the formula:
x = (-54 ± 47.23) / 18
This yields two values:
x₁ = (-54 + 47.23) / 18 ≈ -0.38
x₂ = (-54 – 47.23) / 18 ≈ -5.63
Thus, the zeros of the quadratic function are approximately -0.38 and -5.63.