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Chapter 2: Problem 70
Write the complex number in standard form. $$(2-\sqrt{-6})^{2}$$
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The revenue and cost equations for a product are \(R=x(75-0.0005 x)\) and \(C=30 x+250,000,\) where \(R\) and \(C\) are measured in dollars and \(x\) represents the number of units sold. How many units must be sold to obtain a profit of at least \(\$ 750,000 ?\) What is the price per unit?
Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=x^{2}+36$$
Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-2 x^{3}-3 x^{2}+12 x-18\) (Hint: One factor is \(\left.x^{2}-6 .\right)\)
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 $$f(x)=x^{3}-1$$
Write the polynomial (a) as the product of factors that are irreducible over the rationals, (b) as the product of linear and quadratic factors that are irreducible over the reals, and (c) in completely factored form. \(f(x)=x^{4}-3 x^{3}-x^{2}-12 x-20\) (Hint: One factor is \(\left.x^{2}+4 .\right)\)
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