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Theory of Equations, 5

__Category__: Algebra

"Published in Newark, California, USA"
Find the remaining roots of the equation
if -√2 is a root.
__Solution__:
If
one of the root of the equation is given which is -√2, then we need
to get its conjugate because we want to eliminate the radical sign
in the given equation. The conjugate of -√2 is √2. Hence, the
equation or a factor from the product of a root and its conjugate is
In order to get the other factor for the given equation, let's divide the given equation with the above equation, we have
Since there's no remainder in the division, then the other factor of the given equation is x² - 2x + 4.
By using the completing the square method, we can solve for the other roots of the given equation as follows
Therefore, the other roots of the given equation are and .