To find the roots of the quadratic function \( f(q) = q^2 - 125 \), we need to set the function equal to zero:
\[ q^2 - 125 = 0 \]
This can be rewritten as:
\[ q^2 = 125 \]
Taking the square root of both sides, we find:
\[ q = \sqrt{125} \quad \text{or} \quad q = -\sqrt{125} \]
Since \( \sqrt{125} = \sqrt{25 \cdot 5} = 5\sqrt{5} \), the roots can be expressed as:
\[ q = 5\sqrt{5} \quad \text{and} \quad q = -5\sqrt{5} \]
Thus, the roots of the function are:
- \( q = 5\sqrt{5} \)
- \( q = -5\sqrt{5} \)
From your options, the correct choices are:
- \( q = 55\sqrt{5} \) (this seems like a typo, it should be \( q = 5\sqrt{5} \))
- \( q = -5\sqrt{5} \)
So the final roots are:
- \( q = 5\sqrt{5} \)
- \( q = -5\sqrt{5} \)