By Brian Osserman
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Additional info for A Galois theory example
The complete solution is t = -3, 3. 2 Type V t2 = -4 is impossible. If v'2x + 3 + v'6x- 2 = 7 This is quite a difficult equation to solve. For the moment, let A= v'2x + 3 and B = v'6x- 2. e. [ has not yet been removed, and so both sides must be squared again. ) :. 5 30 MASTERING ADVANCED PURE MATHEMATICS It would appear that there are two answers, but you have squared the original equation twice, and this may produce problems. 5 + 3 + V6 But 10 + 17 =f. 5- 2 = 7? Hence x = 3 is the only solution.
Has not yet been removed, and so both sides must be squared again. ) :. 5 30 MASTERING ADVANCED PURE MATHEMATICS It would appear that there are two answers, but you have squared the original equation twice, and this may produce problems. 5 + 3 + V6 But 10 + 17 =f. 5- 2 = 7? Hence x = 3 is the only solution. Exercise 2 ( c J - - - - - - - - - - - - - - - - - - - - - - - . 4 The quadratic polynomial The expression ax 2 + bx +cis a polynomial of degree 2. However, it is usually referred to as a quadratic expression (or quadratic function).
The following notation is used to avoid the confusion. The greek letter l: (Sigma) is used to denote 'find the sum'. 100 Hence 1 + 2 + 3 + ... + 100 = 2:::> r=l The expression r represents the rth term (T,) in the series, and the instruction above and below the sigma sign means you start at r = 1, increase r by one each time, substitute into the expression for the rth term, and add up the results until r reaches 100. In the above example, T 1 is the first term, that is, T 1 = l. T2 is the second term, that is, T2 = 2, and so on.
A Galois theory example by Brian Osserman