Math Problem Statement
1.) X² + 6x + 3 = 0 a= 1 b= 6 c= 3 X1 + X2 = -b/a = -(6)/1 = -6
Solution
You are calculating the sum of the roots of the quadratic equation using the relationship between the coefficients and the roots. Here’s a detailed explanation:
Given the general form of the quadratic equation , the sum of the roots is given by:
For your equation :
So, the sum of the roots is:
This is correct. The sum of the roots is indeed .
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:
- How can we find the product of the roots of a quadratic equation?
- What is the quadratic formula, and how is it derived?
- How can we factorize quadratic equations when factoring is possible?
- How do the discriminant and the nature of roots relate?
- Can we solve this equation graphically?
Tip: The discriminant () of a quadratic equation helps you determine if the roots are real or complex.
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Math Problem Analysis
Mathematical Concepts
Algebra
Quadratic Equations
Sum of Roots
Formulas
Quadratic equation formula ax^2 + bx + c = 0
Sum of roots formula: -b/a
Theorems
Relation between roots and coefficients
Suitable Grade Level
Grades 7-9