Stitz-Zeager_College_Algebra_e-book

2 complex numbers include things youd normally expect

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Unformatted text preview: quadratic in disguise’ provided that there are exactly three terms and the exponent of the first term is exactly twice that of the second. It is entirely possible that a polynomial has no real roots at all, or worse, it has real roots but none of the techniques discussed in this section can help us find them exactly. In the latter case, we are forced to approximate, which in this subsection means we use the ‘Zero’ command on the graphing calculator. We now present other theorems and discuss how to find zeros of polynomials when we do not have access to a graphing calculator. 3.3.2 For Those Wishing NOT to use a Graphing Calculator Suppose we wish to find the zeros of f (x) = 2x4 + 4x3 − x2 − 6x − 3 without using the calculator. In this subsection, we present some more mathematical tools to help us. Our first result is due to Ren´ Descartes and gives us an estimate of how many positive and how many negative real zeros e are to be found. The theorem requires us to discuss what is meant by the variation...
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