Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 8 - Section 8.3 - Solving Equations by Using Quadratic Methods - Exercise Set: 40

Answer

The solutions are $-i, i,$ and $3$.

Work Step by Step

Group the first two terms together and the last two terms together to obtain: $(x^3+x)+(-3x^2-3)=0$ Factor out the GCF in each group ($x$ in the first and $-3$) to obtain: $x(x^2+1)+(-3)(x^2+1)$ Factor out the GCF of the expression ($x^2+1$) to obtain: $=(x^2+1)[x+(-3)] \\=(x^2+1)(x-3)$ Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain: \begin{array}{ccc} \\&x^2+1=0 &\text{or} &x-3=0 \\&x^2=-1 &\text{or} &x=3 \\&x=\pm\sqrt{-1} &\text{or} &x=3 \\&x=\pm i &\text{or} &x=3 \end{array} Therefore, the solutions are $-i, i,$ and $3$.
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