+0  
 
0
153
1
avatar+558 

What does the fundamental theorem of algebra state about the equation 2x2+8x+14=0

 

SamJones  Mar 4, 2018
 #1
avatar+2180 
+1

The following diagram illustrates the gist of the Fundamental Theorem of Algebra.

 

 \(P(x)=\underbrace{ax^n+bx^{n-1}+cx^{n-2}+...+yx+z}\\ \hspace{30mm}\text{n complex roots}\)

 

The degree of the polynomial of \(2x^2+8x+14\) is 2, so the number of complex roots is also 2. 

 

You can use the quadratic formula to find those roots.

 

\(2x^2+8x+14=0\) Apply the quadratic formula!
\(x_{1,2}=\frac{-8\pm\sqrt{8^2-4*2*14}}{2*2}\) Now it is a matter of simplifying. 
\(x_{1,2}=\frac{-8\pm\sqrt{64-112}}{4}\)  
\(x_{1,2}=\frac{-8\pm\sqrt{-48}}{4}\)  
\(x_{1,2}=\frac{-8\pm\sqrt{48*-1}}{4}\)  
\(x_{1,2}=\frac{-8\pm i\sqrt{48}}{4}\)  
\(x_{1,2}=\frac{-8\pm i\sqrt{16*3}}{4}\)  
\(x_{1,2}=\frac{-8\pm 4i\sqrt{3}}{4}\)  
\(x_{1,2}=-2\pm i\sqrt{3}\)  
   
TheXSquaredFactor  Mar 4, 2018

49 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.