A Key to Day's Algebra |
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1st Rem 2d Rem assumed series CC-BD Changing the signs Clearing of fractions Coeff comp Completing the square continued fraction cubic equation derived polynomial Divide this remainder Equating these values equation whose roots EXAMPLE Expanding Extracting the root Extracting the square extremes and means Find the roots Find the sum formula fract greatest common divisor Horner's Method Involving both sides known term last divisor Let x lower equation Mult multiply the last Multiply this remainder Multiplying extremes number of acres number of gallons number of yards order of diff positive root PROB Prod Proposed series quadratic equation quantity quotient real roots Reduce remaining roots required equation required roots Restoring the values Rule given series of signs square root Squaring each side Sturm's Theorem Subst Substituting this value supposition Trans Transposing and uniting triangle uniting terms xy³
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Page 57 - This process of adding the square of half the coefficient of the first power of the unknown quantity to the first member, in order to make it a perfect square, is called COMPLETING THE SQUARE.
Page 167 - Hence we perceive, 1. The coefficient of the second term of any equation is equal to the sum of all the roots with their signs changed. 2. The coefficient of the third term is equal to the sum of the products of all the roots taken two and two.
Page 57 - In the third and fourth forms, when q is greater thanp2, that is, when the known term is negative, and greater than the square of half the coefficient of the first, power of X, both values of the unknown quantity are impossible.
Page 126 - Ex. 3. Find the equation whose roots are greater by 3 than those of the equation x4+9x3+12x2— 14x=0.
Page 110 - Ex. 6. Find the nth term of the series 1, 3, 6, 10, 15, 21, etc. Ex. 7. Find the nth term of the series 1, 4, 10, 20, 35, etc.
Page 82 - ... geometrical progression. 375. Problems in geometrical progression may be solved, as in other parts of algebra, by means of equations. Prob. 10. Find three numbers in geometrical progression, such that their sum shall be 14, and the sum of their squares 84. Let the three numbers be x, y and z. By the conditions, x: y :: y: z, or xz=y z And x-\-y+z=14i And a; 2 -fy 2 +z 2 =84 . Ans.
Page 112 - ... the number of terms employed. EXAMPLES. 1. Find the sum of 15 terms of the series 2. Find the sum of 20 terms of the series 1, 4, 10, 20, 35, etc. 3. Find the sum of n terms of the series 1, 2, 3, 4, 5, 6, etc.
Page 37 - Let x = the greater number, and y the less. By the conditions, x + у = 80, and у — ж+y:2ж — y::l:7 Uy — 7x=2x— у 15y = 9ж, and ->y = За: 3« + 3y = 80 x 3 8y = ЯП xu, (Hid у = 30.
Page 55 - Let x •=. the number of miles A travelled : then, x — 18= the number of miles В travelled.
Page 137 - The equation cannot have more than two positive roots, since it has only two variations.