Elements of Algebra: On the Basis of M. Bourdon, Embracing Sturm's and Horner's Theorems : and Practical Examples |
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Page 50
... derived , without reduction , from the multiplication of a term of the divisor by a term of the quotient . Therefore ... polynomial is the product of two or more factors , it is often desirable to resolve it into its component ...
... derived , without reduction , from the multiplication of a term of the divisor by a term of the quotient . Therefore ... polynomial is the product of two or more factors , it is often desirable to resolve it into its component ...
Page 333
... polynomial which is derived from another by the law just explained , is called a derived polynomial . Recollect that X is what the given polynomial becomes when x is substituted for x . Y ' is called the first ... DERIVED POLYNOMIALS .
... polynomial which is derived from another by the law just explained , is called a derived polynomial . Recollect that X is what the given polynomial becomes when x is substituted for x . Y ' is called the first ... DERIVED POLYNOMIALS .
Page 334
... derived polynomial . 2. Let it be required to cause the second term to disappear in the equation x4 12x3 + 17x2 – 9x + 7 = 0 . Make ( Art . 263 ) , 12 x = u + = u +3 ; 4 whence , x = 3 . The transformed equation will be of the form Z X ...
... derived polynomial . 2. Let it be required to cause the second term to disappear in the equation x4 12x3 + 17x2 – 9x + 7 = 0 . Make ( Art . 263 ) , 12 x = u + = u +3 ; 4 whence , x = 3 . The transformed equation will be of the form Z X ...
Page 336
... derived polynomials of this member . With respect to the second member , it follows from Art . 251 : 1st . That the term involving uo , or the last term , is equal to the ... derived polynomial 336 [ CHAP . X. ELEMENTS OF ALGEBRA .
... derived polynomials of this member . With respect to the second member , it follows from Art . 251 : 1st . That the term involving uo , or the last term , is equal to the ... derived polynomial 336 [ CHAP . X. ELEMENTS OF ALGEBRA .
Page 337
... derived polynomial , divided by 2 , is equal to the sum of the products of the m factors of the first member of the proposed equation , taken m 2 and m - 2 ; or equal to the sum of the quotients obtained by dividing X by each of the ...
... derived polynomial , divided by 2 , is equal to the sum of the products of the m factors of the first member of the proposed equation , taken m 2 and m - 2 ; or equal to the sum of the quotients obtained by dividing X by each of the ...
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Common terms and phrases
algebraic quantity approximating fraction arithmetical arithmetical progression becomes binomial formula called co-efficient common difference continued fraction contrary signs cube root deduce denote the number derived polynomial divide dividend division entire number equal example exponent extract the square figures Find the square find the values following RULE formula given equation given number gives greatest common divisor hence indicated inequality irreducible fraction last term leading letter least common multiple less logarithm monomial multiplicand multiplied negative roots nth power nth root number of terms obtain operation perfect square positive roots preceding problem progression proposed equation quotient radical sign real roots Reduce remainder required root required to find result second degree second member second term simplest form square root subtract superior limit suppose taken third transformed equation unknown quantity whence whole number X₁
Popular passages
Page 99 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Page 364 - VARIATIONS of signs, nor the number of negative roots greater than the number of PERMANENCES. Consequence. 328. When the roots of an equation are all real, the number of positive roots is equal to the number of variations, and the number of negative roots to , the number of permanences.
Page 118 - X 6 62 + 3 x 3; and taken 3 tens times, 32 + 2 (3 X 6) + 6s gives 3 x 6 + 32 ; and their sum is, 33 + 2 (3 x 6) + 63 : that is, Rule. — The square of a number is equal to the square of the tens, plus twice the product of the tens by the units, plus the square of the units.
Page 174 - Find the value of one of the unknown quantities, in terms of the other and known quantities...
Page 39 - That is, the square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.
Page 200 - Subtract the cube of this number from the first period, and to the remainder bring down the first figure of the next period for a, dividend.
Page 242 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 215 - Resolve the quantity under the radical sign into two factors, one of which is the highest perfect power of the same degree as the radical. Extract the required root of this factor, and prefix the result to the indicated root of the other.
Page 41 - Divide the coefficient of the dividend by the coefficient of the divisor.
Page 10 - Logic is a portion of the art of thinking; language is evidently, and by the admission of all philosophers, one of the principal instruments or helps of thought; and any imperfection in the instrument or in the mode of employing it is confessedly liable, still more than in almost any other art, to confuse and impede the process and destroy all ground of confidence in the result.