The formula for the sum of the roots of a quadratic equation is derived from the standard form of the quadratic equation:

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

If \( r_1 \) and \( r_2 \) are the roots of the quadratic equation, then the sum of the roots can be expressed as:

\[
\text{Sum of the roots} = r_1 + r_2 = -\frac{b}{a}
\]

This formula comes from Vieta's formulas, which relate the coefficients of a polynomial to sums and products of its roots.

Would you like more details or have any other questions?

Here are 8 related questions to expand on this topic:

1. How is the product of the roots of a quadratic equation calculated?
2. Can the sum of the roots be used to determine the vertex of the parabola?
3. How does changing the coefficient \( b \) in the quadratic equation affect the sum of the roots?
4. What happens to the sum of the roots if the quadratic equation is multiplied by a constant?
5. How does the sum of the roots change when the quadratic equation is expressed in vertex form?
6. Can you derive the sum of the roots for cubic or higher-degree polynomials?
7. How does the quadratic formula relate to the sum and product of the roots?
8. What are Vieta's formulas, and how do they apply to other types of polynomials?

**Tip:** Remember that the sum of the roots is independent of the constant term \( c \) in the quadratic equation!

Explore the formula for the sum of the roots of a quadratic equation, derived from Vieta's formulas. This explanation covers the relationship between coefficients and roots, suitable for Grades 9-12.

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