To find the roots of the quadratic function f(x) = x² – 62x + 22, we can use the quadratic formula:
x = (-b ± √(b² – 4ac)) / 2a
In this function, the coefficients are:
- a = 1
- b = -62
- c = 22
Firstly, we calculate the discriminant:
b² – 4ac = (-62)² – 4(1)(22)
= 3844 – 88 = 3756
Now, plug the values into the quadratic formula:
x = (62 ± √3756) / 2
Next, we need to calculate the square root of 3756:
√3756 ≈ 61.3
Now we substitute back into the formula:
x₁ = (62 + 61.3) / 2 ≈ 61.65
x₂ = (62 – 61.3) / 2 ≈ 0.35
Thus, the roots of the equation f(x) = x² – 62x + 22 are approximately:
- x₁ ≈ 61.65
- x₂ ≈ 0.35