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... Solving Polynomial EquationsAlgebraic Method • Set Polynomial Equation equal to zero. • Factor the resulting polynomial expression into a product of linear expressions. • Reduce the equation to a series of linear equations. This is a classic example of analytic reasoning – reducing a more complex p ...
... Solving Polynomial EquationsAlgebraic Method • Set Polynomial Equation equal to zero. • Factor the resulting polynomial expression into a product of linear expressions. • Reduce the equation to a series of linear equations. This is a classic example of analytic reasoning – reducing a more complex p ...
Solutions to problem sheet 4.
... (b) 3 − i = 2e−πi/6 . Hence one root is α = (2)1/7 e−iπ/42 . Hence every root is of the form αω for one of the 7th roots of unity. Hence it is one of the seven complex numbers ei(12k−1)π/42 for k = 0, 1, . . . , 6. (c) By standard trigonometry it is enough to show that the three sides of the triangl ...
... (b) 3 − i = 2e−πi/6 . Hence one root is α = (2)1/7 e−iπ/42 . Hence every root is of the form αω for one of the 7th roots of unity. Hence it is one of the seven complex numbers ei(12k−1)π/42 for k = 0, 1, . . . , 6. (c) By standard trigonometry it is enough to show that the three sides of the triangl ...
Chapter R - Reference R.1 Study Tips 1. Before the Course 2
... 1. Before the Course 2. During the Course 3. Preparation for Exams 4. Where to Go for Help ...
... 1. Before the Course 2. During the Course 3. Preparation for Exams 4. Where to Go for Help ...
Quadratic and Linear System
... 5. Let’s apply it to our problem. We can substitute the linear equation into the quadratic equation for y. Why can we do this? Because both of our equations are y = something so we can just set them equal to each other as we substitute one equation in for the other. 6. Once you have done that, you ...
... 5. Let’s apply it to our problem. We can substitute the linear equation into the quadratic equation for y. Why can we do this? Because both of our equations are y = something so we can just set them equal to each other as we substitute one equation in for the other. 6. Once you have done that, you ...
Algebra II Trig Content Correlation
... polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11] AIIT.7. Use the structure of an expression to identify ways to rewrite it. [A-SSE2] AIIT.17. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate ...
... polynomial, rational, absolute value, exponential, and logarithmic functions.* [A-REI11] AIIT.7. Use the structure of an expression to identify ways to rewrite it. [A-SSE2] AIIT.17. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.