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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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