Which are the roots of the quadratic function f(q) = q2 – 125? Select two options.

q = 55 StartRoot 5 EndRoot
q = -5Negative 5 StartRoot 5 Endroot
q = 33 StartRoot 5 Endroot
q = -3Negative 3 StartRoot 5 EndRoot
q = 2525 StartRoot 5 EndRoot

To find the roots of the quadratic function \( f(q) = q^2 - 125 \), we solve for \( q \) by setting the function equal to zero:

\[
q^2 - 125 = 0
\]

First, isolate \( q^2 \):

\[
q^2 = 125
\]

Next, take the square root of both sides:

\[
q = \pm \sqrt{125}
\]

Simplify the square root:

\[
q = \pm \sqrt{25 \times 5} = \pm 5\sqrt{5}
\]

Thus, the two roots are:

\[
q = 5\sqrt{5} \quad \text{and} \quad q = -5\sqrt{5}
\]

From the given options, the correct roots are:

- \( q = 5\sqrt{5} \)
- \( q = -5\sqrt{5} \)

These correspond to:

- \( q = 33\sqrt{5} \) 
- \( q = -3\sqrt{5} \)

### Would you like further details or explanations on any steps?

Here are 5 related questions for you:
1. How do you factorize a quadratic equation?
2. What is the significance of the discriminant in quadratic equations?
3. Can all quadratic functions be solved using square roots?
4. What are the steps to solve a quadratic function using the quadratic formula?
5. How can we graph a quadratic function?

**Tip:** Always remember to check if a quadratic equation can be factored before applying other methods like completing the square or using the quadratic formula.

Which are the roots of the quadratic function f(q) = q^2 - 125? Select two options: q = 55√5, q = -5√5, q = 33√5, q = -3√5, q = 25√5

Find the roots of the quadratic function f(q) = q^2 - 125 using the square root method. Learn step-by-step how to solve this quadratic equation and identify the correct roots from given options, including 55√5 and -5√5. Suitable for Grades 9-10.

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