The sum of the roots of a quadratic equation in the standard form ax² + bx + c = 0 can be found using the formula -b/a.
Here's a breakdown:
Understanding the Quadratic Equation
A quadratic equation is generally expressed as:
- ax² + bx + c = 0
Where:
- x is the variable (or unknown)
- a, b, and c are constants, with a ≠ 0.
- The roots of the equation are the values of x that satisfy the equation (i.e., make the equation true). A quadratic equation has two roots (which may be real and distinct, real and equal, or complex conjugates).
The Formula for the Sum of the Roots
Let the two roots of the quadratic equation be x₁ and x₂. Then, the sum of the roots is given by:
- x₁ + x₂ = -b/a
Example
Consider the quadratic equation: 2x² + 5x - 3 = 0
Here:
- a = 2
- b = 5
- c = -3
The sum of the roots is:
- -b/a = -5/2
Therefore, the sum of the roots of the equation 2x² + 5x - 3 = 0 is -5/2.
In Summary
To find the sum of the roots of a quadratic equation ax² + bx + c = 0, simply divide the negative of the coefficient of the x term (b) by the coefficient of the x² term (a). The formula is -b/a.
