Find all rational, irrational and complex zeros (and state their multiplicities) of the polynomial function P(x)=x4+15x2−54. 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+15x2−54=(x2+18)(x2+3)
To get the zeros, we set x2+18=0 and x2+3=0 so,
x2=−18andx2=−3x=±√−18x2=±√−3x=±3√2ix=±√3i
Thus, the complex zeros are 3√2i,−3√2i,√3i and −√3i. All the zeros have multiplicity of 1.
No comments:
Post a Comment