Question

which are the roots of the quadratic function $f(q) = q^2 - 125$? select two options.
$\square$ $q = 5\sqrt{5}$
$\square$ $q = -5\sqrt{5}$
$\square$ $q = 3\sqrt{5}$
$\square$ $q = -3\sqrt{5}$
$\square$ $q = 25\sqrt{5}$

Explanation:

Step1: Set function to zero

To find roots, set \( f(q) = 0 \), so \( q^2 - 125 = 0 \).

Step2: Solve for \( q \)

Add 125 to both sides: \( q^2 = 125 \). Take square roots: \( q = \pm\sqrt{125} \). Simplify \( \sqrt{125} = \sqrt{25\times5} = 5\sqrt{5} \), so \( q = 5\sqrt{5} \) or \( q = -5\sqrt{5} \).

Answer:

A. \( q = 5\sqrt{5} \), B. \( q = -5\sqrt{5} \)