Quadratic formula

Definition

The quadratic formula is used to find the roots of a quadratic equation 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 quadratic formula can always be applied to any quadratic equation, whether it has real or complex solutions.
2. The discriminant ($b^2 - 4ac$) determines the nature of the roots: if positive, there are two distinct real roots; if zero, one real root; and if negative, two complex roots.
3. Derived from completing the square on a general quadratic equation $ax^2 + bx + c = 0$.
4. Quadratic equations can also be solved by factoring and using the square root method, but these methods are not always applicable.
5. When applying the quadratic formula, ensure all terms are first moved to one side of the equation to set it equal to zero.

Review Questions

• What does the discriminant tell you about a quadratic equation's roots?
• Write down and explain each part of the quadratic formula.
• How do you determine which solution method (factoring, completing the square, or quadratic formula) to use for a given quadratic equation?

Related terms

Discriminant:

In a quadratic equation $ax^2 + bx + c = 0$, it is given by $\Delta = b^2 - 4ac$ and determines the nature of the roots.

Complex Roots:

Roots that occur when the discriminant ($b^2 - 4ac$) is negative, resulting in non-real solutions of a quadratic equation.

Completing The Square: A method used to solve a quadratic equation by rewriting it in the form $(x-h)^2 = k$, making it easier to solve for x.