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Chapter 2: Problem 9
Find real numbers \(a\) and \(b\) such that the equation is true. $$(a-1)+(b+3) i=5+8 i$$
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Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$f(x)=-5 x^{3}+x^{2}-x+5$$
Match the cubic function with the numbers of rational and irrational zeros. (a) Rational zeros: \(0 ;\) irrational zeros: 1 (b) Rational zeros: \(3 ;\) irrational zeros: 0 (c) Rational zeros: \(1 ;\) irrational zeros: 2 (d) Rational zeros: \(1 ;\) irrational zeros: 0 $$f(x)=x^{3}-2 x$$
Find all the zeros of the function. When there is an extended list of possible rational zeros, use a graphing utility to graph the function in order to disregard any of the possible rational zeros that are obviously not zeros of the function. $$g(x)=x^{5}-8 x^{4}+28 x^{3}-56 x^{2}+64 x-32$$
(a) Find the interval(s) for \(b\) such that the equation has at least one real solution and (b) write a conjecture about the interval(s) based on the values of the coefficients. $$x^{2}+b x-4=0$$
Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{4}-16$$
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