calculate the roots or need any further explanation?

To calculate the roots of a quadratic equation, we'll use the quadratic formula. The standard form of a quadratic equation is:

\[
ax^2 + bx + c = 0
\]

The quadratic formula to find the roots \(x_1\) and \(x_2\) is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

### Steps to Calculate the Roots:
1. **Identify the coefficients** \(a\), \(b\), and \(c\) from the equation.
2. **Calculate the discriminant** \(D\) using the formula \(D = b^2 - 4ac\).
3. **Determine the nature of the roots**:
   - If \(D > 0\), the equation has two distinct real roots.
   - If \(D = 0\), the equation has exactly one real root (a repeated root).
   - If \(D < 0\), the equation has two complex roots.
4. **Apply the quadratic formula** to find the roots.

If you provide the specific quadratic equation or its coefficients \(a\), \(b\), and \(c\), I can calculate the roots for you.

Would you like to proceed with an example, or do you have a specific equation in mind?

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Here are 8 related questions that expand on this topic:
1. What happens when the discriminant is negative?
2. How can the quadratic formula be derived?
3. How does the quadratic formula change if \(a = 1\)?
4. Can you solve a quadratic equation using factorization?
5. What are the applications of quadratic equations in real life?
6. How do you find the vertex of a quadratic function?
7. What is the axis of symmetry in a quadratic equation?
8. How can quadratic equations be solved graphically?

**Tip:** Always check the discriminant first; it quickly tells you about the nature of the roots without fully solving the equation.

Learn how to calculate the roots of a quadratic equation using the quadratic formula. Understand the discriminant and how it determines the nature of the roots. Detailed step-by-step explanation and examples provided.

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