The Elements of Algebra |
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... Quadratic Equations 98 Problems 131 CHAPTER IV . Surds 154 Binomial Quadratic Surds 160 CHAPTER V. Ratio 167 Proportion 172 Variation 178 Arithmetic Series CHAPTER VI . Geometric Series Harmonic Progression PAGE.
... Quadratic Equations 98 Problems 131 CHAPTER IV . Surds 154 Binomial Quadratic Surds 160 CHAPTER V. Ratio 167 Proportion 172 Variation 178 Arithmetic Series CHAPTER VI . Geometric Series Harmonic Progression PAGE.
Page 98
... QUADRATIC EQUATIONS . 89. Quadratic equations are of two kinds . ( 1 ) Pure quadratics , which are of the form ax2 = b , or which do not involve the simple power of the unknown quantity . ( 2 ) Adfected quadratics , which are of the ...
... QUADRATIC EQUATIONS . 89. Quadratic equations are of two kinds . ( 1 ) Pure quadratics , which are of the form ax2 = b , or which do not involve the simple power of the unknown quantity . ( 2 ) Adfected quadratics , which are of the ...
Page 99
... QUADRATIC EQUATION . 91. Let ax2 + bx c be the equation , or dividing by a = b x2 + с x = a a b с Instead of put p , and for put q ; a .. x2 + px = q • Now let a quantity r be added to both sides , so that x2 + par shall be a complete ...
... QUADRATIC EQUATION . 91. Let ax2 + bx c be the equation , or dividing by a = b x2 + с x = a a b с Instead of put p , and for put q ; a .. x2 + px = q • Now let a quantity r be added to both sides , so that x2 + par shall be a complete ...
Page 101
... the form x2 + px − q = 0 , we see that in a quadratic equation , the last term is equal to the product of the values of x . This proposition may be thus generalized for an equation of any degree whatever ; EQUATIONS . 101.
... the form x2 + px − q = 0 , we see that in a quadratic equation , the last term is equal to the product of the values of x . This proposition may be thus generalized for an equation of any degree whatever ; EQUATIONS . 101.
Page 102
... quadratic can only have two roots . We may remark that these values are not true at the same time , unless 2 q 2 , and then p = 4 ' 4 0 , and then ɑ = = 3 . And also that , if a be a root of a quadratic , x - a will divide the equation ...
... quadratic can only have two roots . We may remark that these values are not true at the same time , unless 2 q 2 , and then p = 4 ' 4 0 , and then ɑ = = 3 . And also that , if a be a root of a quadratic , x - a will divide the equation ...
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Common terms and phrases
2ab+b² a²+2ab+b² a²x² a³b ab² ab³ algebraical quantities arithmetic mean arithmetic series arithmetical progression ax² binomial coefficient common difference compound cube root decimal denominator digits divided dividend division divisor equal examples expressed Extract the square factor Find the greatest find the numbers Find the sum fraction geometrical progression greatest common divisor greatest common measure Hence last term least common multiple less letters logarithm multiplied negative number of terms numbers in arithmetical P₁ permutations QUADRATIC EQUATIONS quotient ratio remainder result rule shew square root subtract surd third unity unknown quantity whence write written xy³
Popular passages
Page 38 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Page 199 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Page 22 - 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.
Page 173 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.