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

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

SamJones  Mar 4, 2018
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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

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