The Quadratic Equation

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Lesson Summary: 
We review the Quadratic Equation and find the two values of $x$ for which $ax^2+bx+c=0$ is true.
Lesson Inputs: 
Polynomial Function

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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!