American sign language: a student text, units 19-27 by Charlotte Baker-Shenk, Dennis Cokely

By Charlotte Baker-Shenk, Dennis Cokely

Cokely D., Baker-Shenk C. American signal Language.. A scholar textual content, devices 19-27 (Gallaudet college Press, 1991)(ISBN 0930323882)(400dpi)(187s)

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Extra resources for American sign language: a student text, units 19-27

Sample text

F'(x) +2F(x)} = 0 (ii) We can see that x = k is a repeated root of (i) x = k is a single root of (ii) and that Let us illustrate this with an example. Example 1 If x 3 + x 2 - 16x + 20 = 0 is known to ha ve a repeated root x = k, then x = k will also be a root of the equation 34 Further Engineering Mathematics 13x2 +2x -16 = 0 I Substituting x = k in the two equations, we have 3 (ii) X k Subtract (v) x 3 (ii) Subtract (i) X k3 +k 2 -16k +20 = 0 3k 2 +2k -16 = 0 3k 3 +3e -48k +60 = o 3P + 2k 2 - 16k =0 2 ...

In the same way,/(2) = .......... Therefore, if /(x) = 5x 3 - 8x 2 - 7x +6 were divided by (x- 2), the remainder would be zero. Therefore (x - 2) is ................... Programme 1: Theory of Equations 15 a factor of 5x 3 - 8x 2 -7x +6 The basic form of the remainder theorem can be extended to include quadratic divisors. lf f (x), a polynomial of degree n, is divided by (x- a)(x- b), the quotient q(x) will be a polynomial of degree (n - 2) with a remainder of the form (rx +s). f(a) b a =I= b r=---- a-b so that, the remainder rx +s Example = Determine the remainder resulting from dividing x 3 +2x 2 -4x-7 Remainder 16 a- by = .............

Whatever the form of the roots of a cubic equation, one root at least is always........... Programme 2: Theory of Equations 45 If the one real root, x = k, can be found,f(x) can be factorised into (x- k)(ax 2 + px +q) by long division, so that the equation f(x) = 0 becomes (x- k)(ax 2 +px +q) = 0. ·. x = k or ax 2 + px + q = 0 which can always be solved by factors or formula. Example 1 To solve x 3 - x 2 + 2x +4 = 0. First we seek a linear factor by using the remainder theorem f(x) = x 3 -x 2 +2x +4 = [(x -l)x +2]x +4 /(1) = .............

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