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Chapter 2: Problem 75
Write the polynomial as the product of linear factors and list all the zeros of the function. $$f(x)=5 x^{3}-9 x^{2}+28 x+6$$
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Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=f(-x)$$
Write the polynomial as the product of linear factors and list all the zeros of the function. $$h(x)=x^{3}+9 x^{2}+27 x+35$$
(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. $$3 x^{2}+b x+10=0$$
Write the polynomial as the product of linear factors and list all the zeros of the function. $$g(x)=x^{4}-4 x^{3}+8 x^{2}-16 x+16$$
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?
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