The roots of the quadratic function f(b) = b² – 75 can be found by solving the equation for when f(b) = 0. This leads us to:
b² – 75 = 0
To find the roots, we can rearrange the equation to:
b² = 75
Next, we take the square root of both sides:
b = ±√75
We can simplify √75 as follows:
√75 = √(25 × 3) = √25 × √3 = 5√3
Thus, the roots of the function are:
b = 5√3 and b = -5√3
In conclusion, the roots of the quadratic function f(b) = b² – 75 are 5√3 and -5√3.