Vocabulary
Quadratic Formula- The formula x=(-b±√(b² -4ac))/2a used to find the solutions of the quadratic equation ax²+bx+c=0 when a, b, c are real numbers and a≠0.
Discriminant- The expression b²-4ac for the quadratic equation ax²+bx+c=0; also the expression under the radical sign in the quadratic formula.
Discriminant- The expression b²-4ac for the quadratic equation ax²+bx+c=0; also the expression under the radical sign in the quadratic formula.
Essential Information
By completing the square, a formula can be developed to give the solutions to any quadratic equation. It is called the quadratic formula.
The Quadratic Formula
Let a, b, and c be real numbers such that a≠0. The solutions of the quadratic equation ax²+bx+c=0 are x=(-b±√(b² -4ac))/2a.
The Quadratic Formula
Let a, b, and c be real numbers such that a≠0. The solutions of the quadratic equation ax²+bx+c=0 are x=(-b±√(b² -4ac))/2a.
Discriminant
In the quadratic formula, the expression b²-4ac is called the discriminant of the associated equation ax²+bx+c=0.
In the quadratic formula, the expression b²-4ac is called the discriminant of the associated equation ax²+bx+c=0.
The discriminant of a quadratic equation can be used to determine the equation's number and type of solutions.
Using the Discriminant of ax²+bx+c=0
Using the Discriminant of ax²+bx+c=0