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Find the remaining roots of the equation
if 5 + i is a root.
Solution:
If one of the root of the equation is given which is 5 + i, then we need to get its conjugate because we want to eliminate the imaginary number in the given equation. The conjugate of 5 + i is 5 - i. 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 x + 2.
Therefore, the other root of the given equation is - 2.