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Chapter 2: Problem 63
Perform the operation and write the result in standard form. $$\frac{i}{3-2 i}+\frac{2 i}{3+8 i}$$
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Use the given zero to find all the zeros of the function. Function \(f(x)=x^{4}+3 x^{3}-5 x^{2}-21 x+22\) Zero \(-3+\sqrt{2} i\)
Use Descartes's Rule of Signs to determine the possible numbers of positive and negative real zeros of the function. $$f(x)=3 x^{3}+2 x^{2}+x+3$$
Use the position equation $$s=-16 t^{2}+v_{0} t+s_{0}$$ where \(s\) represents the height of an object (in feet), \(v_{0}\) represents the initial velocity of the object (in feet per second), \(s_{0}\) represents the initial height of the object (in feet), and \(t\) represents the time (in seconds). A projectile is fired straight upward from ground level \(\left(s_{0}=0\right)\) with an initial velocity of 160 feet per second. (a) At what instant will it be back at ground level? (b) When will the height exceed 384 feet?
Think About It \(\quad\) A cubic polynomial function \(f\) has real zeros \(-2, \frac{1}{2},\) and \(3,\) and its leading coefficient is negative. Write an equation for \(f\) and sketch its graph. How many different polynomial functions are possible for \(f ?\)
Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=f(2 x)$$
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