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What does the fundamental theorem of algebra illustrate?

What does the fundamental theorem of algebra illustrate?-example-1

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Answer:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

Explanation:

The fundamental theorem of algebra guarantees that a polynomial equation has the same number of complex roots as its degree.

We have to find the roots of this given equation.

If a quadratic equation is of the form
ax^(2)+bx +c=0

Its roots are
\frac{-b+\sqrt{b^(2)-4ac } }{2a} and
\frac{-b-\sqrt{b^(2)-4ac } }{2a}

Here the given equation is
2x^(2)-4x-1 = 0

a = 2

b = -4

c = -1

If the roots are
x_(1) and x_(2), then


x_(1) =
\frac{-2+\sqrt{(-4)^(2)-4* 2* (-1)}}{2* 2}

=
(4 +√(24))/(4)

=
(2+√(6) )/(2)


x_(2) =
\frac{-2-\sqrt{(-4)^(2)-4* 2* (-1)}}{2* 2}

=
(4 +√(8))/(4)

=
(2-√(6) )/(2)

These are the two roots of the equation.

User Jose Fernandez
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