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Solutions to Exercise Sheet 1
Solutions to Exercise Sheet 1

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Casio Calculator Investigation: Solving Systems

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... Extraneous Solutions • As was the case with rational equations, it was necessary to check answers to be sure they verified the original equation. • With radical equations, it is also necessary for two primary reasons: – With an even index, we cannot have a negative radicand (i.e. we cannot take the ...
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Equations and Inequalities: Elementary Problems

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Numerical Solutions of a System of Equations

Previous polynomial equations have included
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... The only possible combination of numbers is 9 and -5, so x2 + 4x – 45 = 0 becomes (x + 9)(x – 5) = 0. And you would set each piece equal to zero to solve for x. BUT, let’s suppose we have the equation x2 = 25. Intuition says that to isolate the variable, we use the inverse operation of the square ro ...
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Solve a quadratic equation Rationalize denominators of fractions
Solve a quadratic equation Rationalize denominators of fractions

Solutions to the exercises, specified in the example of the
Solutions to the exercises, specified in the example of the

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Steps to solving a rational equation

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Solving Equations with Variables on Both Sides

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Student Information Sheet, Fall 2002, Overmann

... 3. (Section R.3) Parts a – c refer to the polynomial 4 x3  9 x 6  1/ 4 x 2  10  x . a. Write the polynomial in descending powers of the variable: _______________________________________________ b. The degree of this polynomial is __________________ c. The leading coefficient of this polynomial i ...
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Systems of Equations by Elimination

Systems of Equations by Elimination
Systems of Equations by Elimination

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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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