1.) X² + 6x + 3 = 0
a= 1  b= 6 c= 3
X1 + X2 = -b/a
              = -(6)/1 = -6

You are calculating the sum of the roots of the quadratic equation \( x^2 + 6x + 3 = 0 \) using the relationship between the coefficients and the roots. Here’s a detailed explanation:

Given the general form of the quadratic equation \( ax^2 + bx + c = 0 \), the sum of the roots \( x_1 + x_2 \) is given by:

\[
x_1 + x_2 = -\frac{b}{a}
\]

For your equation \( x^2 + 6x + 3 = 0 \):
- \( a = 1 \)
- \( b = 6 \)
- \( c = 3 \)

So, the sum of the roots \( x_1 + x_2 \) is:

\[
x_1 + x_2 = -\frac{b}{a} = -\frac{6}{1} = -6
\]

This is correct. The sum of the roots is indeed \(-6\).

Would you like me to help you calculate the individual roots (using the quadratic formula or factoring)? Or is there anything else you'd like to explore?

Here are 5 related questions:
1. How can we find the product of the roots of a quadratic equation?
2. What is the quadratic formula, and how is it derived?
3. How can we factorize quadratic equations when factoring is possible?
4. How do the discriminant and the nature of roots relate?
5. Can we solve this equation graphically?

**Tip:** The discriminant (\(b^2 - 4ac\)) of a quadratic equation helps you determine if the roots are real or complex.

X² + 6x + 3 = 0
a= 1  b= 6 c= 3
X1 + X2 = -b/a = -(6)/1 = -6

Learn how to solve the quadratic equation x² + 6x + 3 using the sum of roots formula. This step-by-step guide covers essential algebra concepts for students in Grades 7-9, focusing on the relationship between coefficients and roots.

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