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 x2+6x+3=0x^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 ax2+bx+c=0ax^2 + bx + c = 0, the sum of the roots x1+x2x_1 + x_2 is given by:

x1+x2=bax_1 + x_2 = -\frac{b}{a}

For your equation x2+6x+3=0x^2 + 6x + 3 = 0:

  • a=1a = 1
  • b=6b = 6
  • c=3c = 3

So, the sum of the roots x1+x2x_1 + x_2 is:

x1+x2=ba=61=6x_1 + x_2 = -\frac{b}{a} = -\frac{6}{1} = -6

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

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 (b24acb^2 - 4ac) 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