How can you find the two other roots of a cubic polynomial if you're given one of the roots (which is a complex number)?

An important rule to remember when dealing with complex numbers is that if the complex number a+bi is a root of a polynomial, then the complex conjugate (a-bi) must also be a root of this polynomial.Therefore the first step to solving this question would be to multiply the two known roots in order to arrive to a quadratic expression. The way we multiply the two roots is like this: (x-(a+bi)) (x-(a-bi)).Once we have arrived to our quadratic expression, we must divide the cubic expression in the question by this quadratic expression in order to find the last root.After completing these steps we will have the three roots : The complex number given to us, its complex conjugate and the remaining root which was found by dividing the cubic equation given to us against the quadratic expression we found.Hope this helps!

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Answered by Guillermo D. Further Mathematics tutor

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