# Find Real Roots of an Equation Given Two of the Complex Conjugate Roots

The equation x^4 - 18x^3 + 121x^2 - 368x + 420=0

has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of :

x^4 - 18x^3 + 121x^2 - 368x + 420

Please can you show all working out including the division part of this problem as I would like to understand the process behind this problem for future use.

Please see the attached file for the fully formatted problem.

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The equation x - 18x + 121x - 368x + 420=0

has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of :

x - 18x + 121x - 368x + 420

Please can you show all working out including the division part of this problem as I would like to understand the process behind this problem for future use.

Solution. Since the equation x^4- 18x^3 + 121x^2- 368x + ...

#### Solution Summary

The real roots for an equation are found given two of the complex conjugate roots. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.