Finding Roots of Quadratic Equations A quadratic equation in the form of ax^2 + bx + c = 0 can be represented graphically as a parabola with its vertex a...
A quadratic equation in the form of ax^2 + bx + c = 0 can be represented graphically as a parabola with its vertex at the point (a, b/2a). The roots of the equation are the values of x that make the equation equal to zero.
There are two main methods for finding these roots: completing the square and factoring.
Completing the Square:
Factoring:
Set each factor equal to zero. This will give us two linear equations: ax + b = 0 and ax - b = 0.
**Solve the linear equations to find the values of a and b. This will give us the roots of the original quadratic equation.
Examples:
Completing the square:
Roots: x = -4 and x = -8
Factoring:
Roots: x = 3 and x = 3
Key Points:
The solutions to a quadratic equation can be found using either method.
Both methods involve factoring the quadratic expression.
The solutions will always be real and distinct (unless the quadratic equation is perfect square)