Wednesday, March 7, 2012

College Algebra, Chapter 4, Chapter Review, Section Review, Problem 60

Find all rational, irrational and complex zeros (and state their multiplicities) of the polynomial function P(x)=x4+15x254. Use Descartes' Rule of signs, the Upper and Lower Bounds Theorem, the Quadratic Formula or other factoring techniques.

To find the zeros, we first factor P to obtain


P(x)=x4+15x254=(x2+18)(x2+3)



To get the zeros, we set x2+18=0 and x2+3=0 so,


x2=18andx2=3x=±18x2=±3x=±32ix=±3i



Thus, the complex zeros are 32i,32i,3i and 3i. All the zeros have multiplicity of 1.

No comments:

Post a Comment