Question

which are the roots of the quadratic function $f(b) = b^2 - 75$? select two options. $\square$ $b = 5\sqrt{3}$ $\square$ $b = -5\sqrt{3}$ $\square$ $b = 3\sqrt{5}$ $\square$ $b = -3\sqrt{5}$ $\square$ $b = 25\sqrt{3}$

Explanation:

Step1: Set function to zero

To find the roots, set \( f(b) = 0 \), so \( b^2 - 75 = 0 \).

Step2: Solve for \( b \)

Add 75 to both sides: \( b^2 = 75 \). Take square roots: \( b=\pm\sqrt{75} \). Simplify \( \sqrt{75}=\sqrt{25\times3}=5\sqrt{3} \), so \( b=\pm5\sqrt{3} \).

Answer:

A. \( b = 5\sqrt{3} \)
B. \( b = -5\sqrt{3} \)