Root (Quadratic Functions)
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
A root of a quadratic equation is a value of x that makes the equation equal to zero. In other words, a root is a solution to the equation ax^2 + bx + c = 0.
The roots are also called x-intercepts because they represent the points where the graph of the quadratic function crosses the x-axis.
Key points about roots:
A quadratic equation can have two real roots, one real root, or no real roots:
Two real roots: The equation has two different values for x that make the equation equal to zero.
One real root: The equation has one value for x that makes the equation equal to zero, and the vertex of the parabola lies on the x-axis.
No real roots: The equation has no real values of x that make the equation equal to zero because the parabola never crosses the x-axis
2 | 1 | 0 |
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The roots of a quadratic equation can be found by methods like:
Factoring (if the quadratic expression is factorable),
The quadratic formula
Completing the square.
Example:
For the quadratic equation x^2 -5x + 6 = 0, the roots can be found by factoring:
(x - 2)(x - 3) = 0
So, the roots are x = 2 and x = 3. These are the values where the quadratic equation equals zero.
In summary, the roots of a quadratic equation are the values of x that make the equation equal to zero, and they represent the points where the graph of the quadratic crosses the x-axis.