The Quadratic Equation

Primary tabs

Lesson Summary: 
We review the Quadratic Equation and find the two values of x for which ax2+bx+c=0 is true.
Lesson Inputs: 
Polynomial Function

SAMPLE LESSON

Sign in for easy to read lessons narrowly focused on a specific subject. All lessons are linked to each other allowing you to easily see the connections between different Calculus concepts. Our unique Calcmap will give you a bird's-eye view of all our lessons and help you see how important concepts are related to each other. All of the formulas are available to our subscribers, but here is a sample of the lesson you will see when you log in:



Lesson: 

Given a polynomial of the form <Sign in to see all the formulas> where <Sign in to see all the formulas>, the Quadratic Equation is the formula

<Sign in to see all the formulas>

We can find the values of x for which <Sign in to see all the formulas> is true. (Let's call the x values where this is true d and e.) Oftentimes we can factor the polynomial into the form <Sign in to see all the formulas> where d and e are some combination of a, b, and c. We immediately see that x=d and x=e are the two value of x that make <Sign in to see all the formulas>. However, factorization can be difficult. What we want is a general formula to find d and e easily.

Fortunately, we can solve the Quadratic Equation. We find that

<Sign in to see all the formulas>

The only limitation of this formula is that <Sign in to see all the formulas>. Otherwise, you will have a negative number under the square root.

As an example try solving <Sign in to see all the formulas>.

Now check out our Quadratic Equation Solver!