Answer:
None of the options are correct
Step-by-step explanation:
Given
[tex]f(q) = q^2 - 125[/tex]
Required
The roots of the function
Since the function is a quadratic function; to get the roots of the function, f(q) must be equal to 0
[tex]f(q) = q^2 - 125[/tex] becomes
[tex]0 = q^2 - 125[/tex]
Make [tex]q^2[/tex] the subject of formula
[tex]125= q^2[/tex]
Rearrange
[tex]q^2 = 125[/tex]
Take square roots of both sides
[tex]\sqrt{q^2} = \sqrt{125}[/tex]
[tex]q = \sqrt{125}[/tex]
Expand the square root of 125
[tex]q = \sqrt{25 * 5}[/tex]
[tex]q = \sqrt{25} * \sqrt{5}[/tex]
q = ±5 [tex]* \sqrt{5}[/tex]
Split into 2
[tex]q = 5 * \sqrt{5}[/tex] or [tex]q = -5 * \sqrt{5}[/tex]
[tex]q = 5 \sqrt{5}[/tex] or [tex]q = -5 \sqrt{5}[/tex]
Hence, the roots of the quadratic function are [tex]q = 5 \sqrt{5}[/tex] or [tex]q = -5 \sqrt{5}[/tex]
