A Treatise on Algebra: By Charles SmithMacmillan and Company, 1888 - 571 sider |
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Resultat 1-5 av 65
Side ix
... Zero and infinite roots 109 • 109 . 112 • 113 Equations not integral 115 Irrational equations 118 • A quadratic equation can only have two roots . 120 Relations between the roots and the coefficients of a quadratic equation 122 ...
... Zero and infinite roots 109 • 109 . 112 • 113 Equations not integral 115 Irrational equations 118 • A quadratic equation can only have two roots . 120 Relations between the roots and the coefficients of a quadratic equation 122 ...
Side 59
... zero , or negative . I. Let b2-4ac 4a2 the expression is = 3 x - 1 ) ( x - 1 ) . √ b2 - 4ac ) . b2-4ac 4a2 may be be positive . Then the two factors of ax2 + bx + c will be rational or irrational according as b2-4ac is or is not a ...
... zero , or negative . I. Let b2-4ac 4a2 the expression is = 3 x - 1 ) ( x - 1 ) . √ b2 - 4ac ) . b2-4ac 4a2 may be be positive . Then the two factors of ax2 + bx + c will be rational or irrational according as b2-4ac is or is not a ...
Side 68
... zero : this proves that a -b is a factor . Ex . 5. Shew that a is a factor of ( a + b + c ) 3- ( a + b + c ) 3 − ( a − b + c ) 3- ( a + b - c ) 3 . - 89. We have proved that xa is a factor of the ex- pression ax + bxanî + can - 2 + ...
... zero : this proves that a -b is a factor . Ex . 5. Shew that a is a factor of ( a + b + c ) 3- ( a + b + c ) 3 − ( a − b + c ) 3- ( a + b - c ) 3 . - 89. We have proved that xa is a factor of the ex- pression ax + bxanî + can - 2 + ...
Side 69
... zero , their continued product cannot be zero , and therefore the given expression cannot vanish for the value x = k , except a itself is zero . 2-2 But , if a is zero , the original expression reduces to bx2¬1 + cx2 - 2 + ...... , and ...
... zero , their continued product cannot be zero , and therefore the given expression cannot vanish for the value x = k , except a itself is zero . 2-2 But , if a is zero , the original expression reduces to bx2¬1 + cx2 - 2 + ...... , and ...
Side 70
... zero . - Thus a − p = 0 , b − q = 0 , c — r = 0 , & c . that is , - a = p , b = q , c = r , & c . Hence , if two expressions of the nth degree in x are equal to one another for more than n values of x , the coefficient of any power of ...
... zero . - Thus a − p = 0 , b − q = 0 , c — r = 0 , & c . that is , - a = p , b = q , c = r , & c . Hence , if two expressions of the nth degree in x are equal to one another for more than n values of x , the coefficient of any power of ...
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a+b+c a₁ arithmetic mean arithmetical progression ax² b₁ binomial Binomial Theorem C₁ Cambridge coefficient contain continued fraction Crown 8vo denominator determinant digits divergent divide divisible divisor Edition equal equation ax example expansion Extra fcap Fcap Find the number Find the sum follows geometrical progression given expression Globe 8vo greater Hence the required infinity letters logarithm MACMILLAN'S Multiply negative nth convergent nth root nth term number of terms obtained P₁ periodic continued fraction positive integer powers prime number Professor prove quadratic equation quadratic surd quotient ratio remainder School Shew Solve the equation square root subtract suppose Theorem Trinity College u₁ unknown quantities white ball whole number zero
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