Finding the Equation of a Polynomial Given That it Has Two Purely Imaginary Roots and One Real Root

It's only fair to share...Share on FacebookTweet about this on TwitterPin on PinterestShare on Google+Share on RedditEmail this to someone

If a cubic polynomialwhereis real, has a real root and two purely complex roots, we can find the value ofand the complex roots by deriving simultaneous equations.

Since the coefficients of the polynomial are real, the purely complex rootsand occur as a complex conjugate pair so that we can writeandIf the real root isthe the polynomial can be written as

Then from considering the coefficients of



and the constant term gives(3)

(3) divided by (2) gives

Then from (1)

Then from (2),


Comments are closed.