Download The Evelyn Wood Seven-Day Speed Reading and Learning Program by Stanley D. Frank PDF

By Stanley D. Frank

Within the age of knowledge overload, this remarkably potent one-week application will educate you to learn quicker and to continue extra of what you learn.

The Evelyn wooden velocity studying and studying courses have taught hundreds of thousands of individuals of every age to greater than double their interpreting pace and raise their comprehension. the following Stanley D. Frank, utilizing a step-by-step technique, outlines and illustrates the studying innovations which are confirmed equipment of having extra, speedier, out of what you learn. This booklet is the surefire solution to:

Double your interpreting velocity enhance your comprehension Take greater notes organize for time cut-off dates very easily Write essentially and concisely

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F'(a) 4. Equation with given roots If rx, ß, y ... are roots, then the equation is (x-rx)(x-ß)(x-y) ... = 0 38 Further Engineering Mathematics 50 Relation between coefficients and roots If ~, ß, y are the roots of x 3 + px 2 +qx +r = 0 ~+ß+y=-p ~ß +ßy +y~ ~ßy In general, if ~' ß, y 0 0 0 = q = -r are roots of the equation PoX" +P1Xn-l +p2xn-l +o oo +Pn-1X +p" = 0 then sum of the roots = - Pt Po sum of products of roots, taken two at a time = - Pl Po sum of products of roots, taken three at a time = - PJ Po sum of products of roots, n at a time = (- 1)" Pn Po 60 Transformation of equations f(x) = ax 4 +bx 3 +cx 2 +dx +c = 0 lf the new roots are the old roots increased by k, ioeo y = x + k, substitute x = y- k and simplify f(y) = a(y-kt +b(y-k) 3 +c(y-k) 2 +d(y-k) +c = 0 etco 7 Reciprocal equations-unaltered when the variable is replaced by its reciprocal.

In Ill, the equationf(x) = 0 has one real root at A and two complex roots corresponding to B and C-these being a pair of conjugate complex roots. 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.

JO 3. Remainder theorem If f(x) = a 1 xn +a2xn-l + ... +anx +an+ I then f (k) = the remainder resulting from dividing f (x) by (x- k). If f(k) = 0, then (x- k) is a factor of f(x). e. f'(a) 4. Equation with given roots If rx, ß, y ... are roots, then the equation is (x-rx)(x-ß)(x-y) ... = 0 38 Further Engineering Mathematics 50 Relation between coefficients and roots If ~, ß, y are the roots of x 3 + px 2 +qx +r = 0 ~+ß+y=-p ~ß +ßy +y~ ~ßy In general, if ~' ß, y 0 0 0 = q = -r are roots of the equation PoX" +P1Xn-l +p2xn-l +o oo +Pn-1X +p" = 0 then sum of the roots = - Pt Po sum of products of roots, taken two at a time = - Pl Po sum of products of roots, taken three at a time = - PJ Po sum of products of roots, n at a time = (- 1)" Pn Po 60 Transformation of equations f(x) = ax 4 +bx 3 +cx 2 +dx +c = 0 lf the new roots are the old roots increased by k, ioeo y = x + k, substitute x = y- k and simplify f(y) = a(y-kt +b(y-k) 3 +c(y-k) 2 +d(y-k) +c = 0 etco 7 Reciprocal equations-unaltered when the variable is replaced by its reciprocal.

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