Advanced AlgebraGinn, 1905 - 285 páginas This book is designed for use in secondary schools and in short college courses. It aims to present in concise but clear form the portions of algebra that are required for entrance to the most exacting colleges and technical schools. The chapters in 'Algebra to Quadratics' are intended for a review of the subject. The rest of the text concentrates on subjects that are most vital, which is why topics that demand a knowledge of calculus for complete comprehension have been omitted. |
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Página ix
... Substitution 111 119. Number of Solutions . 113 120. Solution when neither Equation is Linear 114 121. Equivalence of Pairs of Equations 120 122. Incompatible Equations 121 123. Graphical Representation of Simultaneous Quadratic ...
... Substitution 111 119. Number of Solutions . 113 120. Solution when neither Equation is Linear 114 121. Equivalence of Pairs of Equations 120 122. Incompatible Equations 121 123. Graphical Representation of Simultaneous Quadratic ...
Página 32
... substituted for a letter in an equation reduces it to an identity is said to satisfy the equation . Thus the number 5 satisfies the equation x2 the equation ( x − 3 ) ( x + 4 ) = 0 . - 241. The number satisfies The process of finding ...
... substituted for a letter in an equation reduces it to an identity is said to satisfy the equation . Thus the number 5 satisfies the equation x2 the equation ( x − 3 ) ( x + 4 ) = 0 . - 241. The number satisfies The process of finding ...
Página 33
... substituted for either will satisfy the equa- tion . Thus the equation x - 2 a = 0 is satisfied 2a = 0 is satisfied if x is replaced by х 2 2 a , or if a is replaced by In the former case we have solved for x , that is , have found a ...
... substituted for either will satisfy the equa- tion . Thus the equation x - 2 a = 0 is satisfied 2a = 0 is satisfied if x is replaced by х 2 2 a , or if a is replaced by In the former case we have solved for x , that is , have found a ...
Página 47
... substitution . Special cases occur , as in the case of two variables , where an infinite number of solutions or no solutions exist . Where no solution exists one is led to a self- contradictory equation on application of the rule . See ...
... substitution . Special cases occur , as in the case of two variables , where an infinite number of solutions or no solutions exist . Where no solution exists one is led to a self- contradictory equation on application of the rule . See ...
Página 64
... substituted in the first one to ascertain if any solutions have been introduced which did not satisfy the original equation . Solutions which have been intro- duced in the process of solving an equation , but which do not satisfy the ...
... substituted in the first one to ascertain if any solutions have been introduced which did not satisfy the original equation . Solutions which have been intro- duced in the process of solving an equation , but which do not satisfy the ...
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Términos y frases comunes
a₁ a²b ab² algebraic arithmetical means assume axis b₁ binomial called coefficients column complex numbers constant term continued fraction coördinates COROLLARY corresponding curve decimal determinant digits Divide division divisor equa equal equation ax² exponents expression Extract the square factor Find the 7th following equations following RULE geometrical means graph Hence identity integers irrational numbers least common multiple left-hand member letters linear equation logarithm monomial Multiply negative number nth term obtain operations pair of values pairs of equations perfect square permutations Plot polynomial positive integer quadratic equation quotient radical ratic rational number real number remainder represent result rule of signs satisfy the equation Solution square root Substituting subtract symbols synthetic division THEOREM tion Transpose vanish variable x₁ zero
Pasajes populares
Página 237 - The characteristic of the logarithm of a number greater than 1 is a positive integer or zero, and is one less than the number of digits to the left of the decimal point.
Página 53 - Find the square root of the first term, write it as the first term of the root, and subtract its square from the given polynomial. Divide the first term of the remainder by...
Página 87 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.
Página 54 - Separate the given number into periods of two figures each, beginning from the units' place. 2d. find the greatest number whose square is contained in the left-hand period ; this is the first figure of the required root. >Subtract its square from the first period, and to the remainder bring down the second period for a dividend.
Página 13 - Multiply the divisor by the first term of the quotient and subtract the product from the dividend.
Página 157 - The number of permutations of n things taken r at a time is n!
Página 12 - The square of any polynomial equals the sum of the squares of the terms plus twice the product of each term by each term which follows it.
Página 53 - Divide the first term of the remainder by twice the first term of the root, and add the quotient to the part of the root already found, and also to the trial-divisor.
Página 53 - We next multiply the complete divisor by the last term of the root and subtract the product from the last remainder.
Página 27 - The numerator and denominator of a fraction may be multiplied or divided by the same number without changing the value of the fraction.