University Algebra: Embracing a Logical Development of the Science with Numerous Graded ExamplesA.S. Barnes, 1889 - 320 páginas |
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Página 292
... derivative of Equation ( 1 ) becomes , when for x we substitute r . Hence , we con- clude that when Equation ( 1 ) has two roots equal to r , its derivative has 1 root equal to r ; and conversely , when the derivative has 1 root equal ...
... derivative of Equation ( 1 ) becomes , when for x we substitute r . Hence , we con- clude that when Equation ( 1 ) has two roots equal to r , its derivative has 1 root equal to r ; and conversely , when the derivative has 1 root equal ...
Página 294
... derivative equation is , 7x + 2 0 . 4x3 15x218-7 = 0 . - The greatest common divisor of the first member is , ( x - 1 ) 2 . Hence , the required equation is , x2 - 3x + 2 = 0 ; which may be solved by known rules . the given equation are ...
... derivative equation is , 7x + 2 0 . 4x3 15x218-7 = 0 . - The greatest common divisor of the first member is , ( x - 1 ) 2 . Hence , the required equation is , x2 - 3x + 2 = 0 ; which may be solved by known rules . the given equation are ...
Página 303
... derivative X1 , will have the contrary signs ; and if we substitute for x , a value inappreciably greater than one of the real roots , the signs of X and X , will be the same . 208. Let us arrange the expressions , X , X , X2 , .. X ...
... derivative X1 , will have the contrary signs ; and if we substitute for x , a value inappreciably greater than one of the real roots , the signs of X and X , will be the same . 208. Let us arrange the expressions , X , X , X2 , .. X ...
Página 304
... . As an example , let it be required to fird the number of real roots in the equation , 20+ - 12x2 + 12x 3 = 0 . ― Here , we have , X = x4 12x2 + 12x - 3. Finding C3 - the derivative of X , and suppressing the 304 ELEMENTS OF ALGEBRA .
... . As an example , let it be required to fird the number of real roots in the equation , 20+ - 12x2 + 12x 3 = 0 . ― Here , we have , X = x4 12x2 + 12x - 3. Finding C3 - the derivative of X , and suppressing the 304 ELEMENTS OF ALGEBRA .
Página 305
... derivative of X , and suppressing the factor , 4 , we have , X1 = c3 — 6x + 3. Dividing X by X1 , we find , for a remainder , 62 + 92-3 ; suppressing the factor , 3 , and changing the sign of the result , we have , X2 = 2x2 -3x + 1 ...
... derivative of X , and suppressing the factor , 4 , we have , X1 = c3 — 6x + 3. Dividing X by X1 , we find , for a remainder , 62 + 92-3 ; suppressing the factor , 3 , and changing the sign of the result , we have , X2 = 2x2 -3x + 1 ...
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Términos y frases comunes
algebraic Arithmetic ax² Binomial Formula Clearing of fractions coefficients common difference containing contrary signs cube root Davies denominator denote the number distance dividend divisible equal roots equation whose roots EXAMPLES exponent expressions Extract the square factors Find the cube Find the fourth Find the greatest Find the square following RULE geometrical progression given equation greatest common divisor Hence imaginary indicated irreducible fraction last term least common multiple Let x denote logarithm miles monomial Multiplying both members negative nth root number of terms operation partial fractions polynomial positive preceding problem proportion quotient radical sign real roots Reduce remainder resulting equation roots equal second degree second member second term solved square root STURM'S THEOREM Substituting subtract third Transform the equation Transposing travels unknown quantity Whence whole number write X₁
Pasajes populares
Página 258 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 255 - THE LOGARITHM: of a number is the exponent of the power to which it is necessary to raise a fixed number, to produce the given number. The fixed number is called the base of the system.
Página 136 - Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units.
Página 36 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Página 81 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Página 231 - If four quantities are in proportion, they will be in proportion by COMPOSITION...
Página 72 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.