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Aim is to obtain to obtain state equations in the following form
Aim is to obtain to obtain state equations in the following form

Solving Equations Using Multiplication and Division
Solving Equations Using Multiplication and Division

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... Example 2: Solve (3x – 5)2 + 36 = 0. Note: this has the form au2 + bu + c = 0, where b = 0 and u is an algebraic expression (u = 3x – 5). So first, isolate u2 = (3x – 5)2. Next, take the square root of each side and place a "" symbol in front of the root ...
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... Px   a n x n  a n 1 x n 1  a n 2 x n 2    a 2 x 2  a1 x  a0 with complex coefficients has at least one complex zero. 2. Complete Factorization Theorem: There exist complex numbers such that any polynomial of degree greater than 1 can be written as P( x)  a  x  c1  x  c2   x  c ...
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1 PROBLEM SET 9 DUE: May 5 Problem 1(algebraic integers) Let K

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< 1 ... 391 392 393 394 395 396 397 398 399 ... 449 >

System of polynomial equations

A system of polynomial equations is a set of simultaneous equations f1 = 0, ..., fh = 0 where the fi are polynomials in several variables, say x1, ..., xn, over some field k.Usually, the field k is either the field of rational numbers or a finite field, although most of the theory applies to any field.A solution is a set of the values for the xi which make all of the equations true and which belong to some algebraically closed field extension K of k. When k is the field of rational numbers, K is the field of complex numbers.
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