Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 6 Rational Exponents and Radical Functions - 6.5 Graph Square Root and Cube Root Functions - 6.5 Exercises - Mixed Review - Page 451: 50


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Work Step by Step

Given: $f(x)=x^4+6x^3+14x^2+54x+45$ The possible rational zeros are: $\pm 1, \pm 3, \pm 5, \pm 9,\pm, \pm 45$ We found a zero: $x=-1$. The given equation becomes: $(x+1)(x^3+5x^2+9x+45)=0\\(x+1)[(x^3+5x^2)+(9x+45)]=0\\(x+1)(x^2+9)(x+5)=0\\(x+1)(x+5)(x-3i)(x+3i)=0$ The solutions are: $x=-1\\x=-5\\x=3i\\x=-3i$
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