# How do you find the number of roots for  x^2-4x+4 using the fundamental theorem of algebra?

Jan 4, 2016

The Fundamental Theorem of Algebra simply states for a polynomial that the total number of roots (both real and imaginary ) must equal the value of the highest exponent

#### Explanation:

For this problem, the highest exponent $= 2$, so the Theorem states that there are two roots .

Using factoring ...

${x}^{2} - 4 x + 4 = \left(x - 2\right) \left(x - 2\right)$

So, this polynomial has root $x = 2$ with multiplicity of 2. That simply means that 2 is a double root . Here is a sketch ...

Hope that helps