An Elementary Algebra |
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Page 171
... called a Com- plete Equation of the second degree . 304. Principles . - 1 . Every affected quadratic equation can be reduced to the general form ax2 + bx = c . 18x = 3 Thus , the equation x2 + 27 AFFECTED QUADRATIC EQUATIONS . 171 AFFECTED.
... called a Com- plete Equation of the second degree . 304. Principles . - 1 . Every affected quadratic equation can be reduced to the general form ax2 + bx = c . 18x = 3 Thus , the equation x2 + 27 AFFECTED QUADRATIC EQUATIONS . 171 AFFECTED.
Page 172
... equation ax2 + bx = c is a general form for affected quadratic equations . 2. Affected quadratic equations depend for their solution on the form of a squared binomial . Thus , ( x + a ) 2 = x2 + 2ax + a2 . Here a2 is evidently the ...
... equation ax2 + bx = c is a general form for affected quadratic equations . 2. Affected quadratic equations depend for their solution on the form of a squared binomial . Thus , ( x + a ) 2 = x2 + 2ax + a2 . Here a2 is evidently the ...
Page 173
... equation x + 6x = -8 ? SOLUTION . Completing the square , we obtain ( 2 ) . Extracting the square root , we obtain ( 3 ) . Transposing , we obtain ( 4 ) . Whence ( 5 ) , or x = -2 , and ( 6 ) , or x = -4 . x2 + ... QUADRATIC EQUATIONS . 173.
... equation x + 6x = -8 ? SOLUTION . Completing the square , we obtain ( 2 ) . Extracting the square root , we obtain ( 3 ) . Transposing , we obtain ( 4 ) . Whence ( 5 ) , or x = -2 , and ( 6 ) , or x = -4 . x2 + ... QUADRATIC EQUATIONS . 173.
Page 176
... equation to the form ax + bx = c , in which the coefficients a and b are integral and prime to each other . If the coefficient of x be odd , multiply the equa- tion by four times the coefficient of x2 , and add the ... QUADRATIC EQUATIONS .
... equation to the form ax + bx = c , in which the coefficients a and b are integral and prime to each other . If the coefficient of x be odd , multiply the equa- tion by four times the coefficient of x2 , and add the ... QUADRATIC EQUATIONS .
Page 177
... equation in the Quadratic Form - that is , any equation which contains but two powers of the unknown quan- tity , the exponent of the one power being twice that of the other -can be solved by the application of the rules given for the ...
... equation in the Quadratic Form - that is , any equation which contains but two powers of the unknown quan- tity , the exponent of the one power being twice that of the other -can be solved by the application of the rules given for the ...
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Common terms and phrases
2ab+b² a²+2ab+b² added affected quadratic equation algebraic apples arithmetical means arithmetical progression binomial cents Clear of fractions coefficient Completing the square compound interest contains cube root denominator denote difference Divide dividend division Extracting the square Find the factors Find the greatest Find the least Find the number Find the square Find the sum Find the value find x frac geometrical progression given number greatest common divisor Hence integer least common multiple lowest terms mixed quantity Monomial Multiply number expressed number of dollars number of terms obtain parenthesis polynomial prime factors Principles.-1 PROBLEMS proportion quan quotient radical sign ratio Reduce remainder result rule for solving SECTION similar fractions SIMPLE EQUATIONS simplest form SOLUTION square root subtracted Theorem tions tity Transposing and uniting unknown quantity whence whole number yards
Popular passages
Page 50 - 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.
Page 63 - 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 64 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first by the second, plus the square of the second.
Page 261 - 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 244 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 194 - Art. 338, that in a proportion, either extreme is equal to the product of the means, divided by the other extreme ; and either of the means is equal to the product of the extremes, divided by the other mean.
Page 218 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel, in going 120 yards ; but if the circumference of each wheel be increased...
Page 64 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 43 - Multiply each term of the multiplicand by each term of the multiplier, and add the partial products.
Page 113 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.