Quadratic formula

Definition

The quadratic formula is a method for solving quadratic equations of the form $ax^2 + bx + c = 0$. It is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

5 Must Know Facts For Your Next Test

1. The discriminant $b^2 - 4ac$ determines the nature of the roots: if positive, two real roots; if zero, one real root; if negative, two complex roots.
2. The quadratic formula can be derived from completing the square on the general form of a quadratic equation.
3. It is applicable to any quadratic equation, regardless of whether it can be factored easily or not.
4. When using the quadratic formula, ensure that all terms are correctly substituted and simplified to avoid errors in calculation.
5. In trigonometric equations involving squared terms, the quadratic formula may be used to solve for angles.

Review Questions

• What does the discriminant tell you about the nature of the solutions to a quadratic equation?
• How would you use the quadratic formula to solve $3x^2 + 6x - 9 = 0$?
• In what scenarios is it beneficial to use the quadratic formula over factoring?

Related terms

Discriminant: The expression $b^2 - 4ac$ in a quadratic equation that determines the number and type of roots.

Completing The Square: A method used to solve a quadratic equation by converting it into a perfect square trinomial.

Roots of an Equation: Values of x that satisfy an equation, making it true when substituted back into the equation.