Understanding Quadratic Equation Roots
In a quadratic equation (where ), the roots of the equation are the values of that make the equation true. A quadratic equation always has two roots that can be found using the formula:
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In a quadratic equation (where ), the roots of the equation are the values of that make the equation true. A quadratic equation always has two roots that can be found using the formula:
The value is called the determinant or discriminant (denoted by ), which is very important because it determines the type of roots of the quadratic equation.
If (or ), then the quadratic equation has two different real roots.
Example:
If (or ), then the quadratic equation has one real repeated root (two roots with the same value).
Example:
If (or ), then the quadratic equation has two different complex (imaginary) roots.
Where is the imaginary number.
Example:
If and are the roots of the quadratic equation , then:
This is an important relationship that can be used to find the coefficients of a quadratic equation if its roots are known.