Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 2 - Cumulative Test for Chapters P-2 - Page 236: 23


$x=0$: $x=2i$: $x=-2i$: $x=-12$

Work Step by Step

$x^4+12x^3+4x^2+48x=0$ $x(x^3+12x^2+4x+48)=0$ $x[x^2(x+12)+4(x+12)]=0$ $x(x^2+4)(x+12)=0$ $x=0$ $x^2+4=0$ $x^2=-4$ $x=±\sqrt {-4}=±2i$ $x+12=0$ $x=-12$ Check the solutions: $x=0$: $0^4+12(0)^3+4(0)^2+48(0)=0+0+0+0=0$ $x=2i$: $(2i)^4+12(2i)^3+4(2i)^2+48(2i)=16-96i-16+96i=0$ $x=-2i$: $(-2i)^4+12(-2i)^3+4(-2i)^2+48(-2i)=16+96i-16-96i=0$ $x=-12$ $(-12)^4+12(-12)^3+4(-12)^2+48(12)=12^4-12^4+576-576=0$
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