A Companion to Wrigley's Collection of Examples: Being Illustrations of Mathematical Processes and Methods of Solution |
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... roots are real , and lie as follows { -2 , -1 } ; { − 1 , 0 } ; { 1 , 2 } ; { 1 , 2 } . - 90 ( 19 ) The signs in X5 , X6 , X7 should all be changed ; hence there will be 2 pairs of imaginary roots , and the 3 real roots will be found ...
... roots are real , and lie as follows { -2 , -1 } ; { − 1 , 0 } ; { 1 , 2 } ; { 1 , 2 } . - 90 ( 19 ) The signs in X5 , X6 , X7 should all be changed ; hence there will be 2 pairs of imaginary roots , and the 3 real roots will be found ...
Page 15
... . .. x = - = = { 3 ± √ = 7 } , or = I + x5 4 ( 1 + x ) s = α , or 4 ( 1 + x ) ( 1 − x + x2 - 203 +24 ) ( I I ( 1 + x ) ( 1 + 4x + бx2 + 4x3 + x4 ) I is a root . = α a ; Also - 1 − x + x2 - ∞3 + QUADRATIC EQUATIONS . 15 1133 9 4,
... . .. x = - = = { 3 ± √ = 7 } , or = I + x5 4 ( 1 + x ) s = α , or 4 ( 1 + x ) ( 1 − x + x2 - 203 +24 ) ( I I ( 1 + x ) ( 1 + 4x + бx2 + 4x3 + x4 ) I is a root . = α a ; Also - 1 − x + x2 - ∞3 + QUADRATIC EQUATIONS . 15 1133 9 4,
Page 64
... root = 4112 . ..the sq . root = 62te . 14 . Let be the radix of the scale , γ then 24 + 32 + 5 = 4954 , or 4+ 3 7.2 = 4949 2 2 whence r = 7 . 16 . Here we have to express 1719 by means 64 SCALES OF NOTATION .
... root = 4112 . ..the sq . root = 62te . 14 . Let be the radix of the scale , γ then 24 + 32 + 5 = 4954 , or 4+ 3 7.2 = 4949 2 2 whence r = 7 . 16 . Here we have to express 1719 by means 64 SCALES OF NOTATION .
Page 69
... roots with their signs changed = − ( − 2 ) . ( − 1 ) . ( 1 ) + ( − 2 ) . ( − 1 ) ( 3 ) + ( − 2 ) ( − 1 ) ( 4 ) ... roots of the equation . Ex . 2 . 1. The equation is then divisible by x - 4 ; to find the quotient . Division .I 1 ...
... roots with their signs changed = − ( − 2 ) . ( − 1 ) . ( 1 ) + ( − 2 ) . ( − 1 ) ( 3 ) + ( − 2 ) ( − 1 ) ( 4 ) ... roots of the equation . Ex . 2 . 1. The equation is then divisible by x - 4 ; to find the quotient . Division .I 1 ...
Page 70
... roots be a , a , b . Then a + a + b = 7 , and a ( a + b ) + ab = 16 ; .. a2 + 2ab , or a2 + 2a ( 7 − 2a ) = 16 ; · .. 3a2 – 14a + 16 , or ( 3a - 8 ) ( a− 2 ) = 0 . - Hence the roots are 2 , 2 , 3 . 11. Let the roots be ad , a , and a ...
... roots be a , a , b . Then a + a + b = 7 , and a ( a + b ) + ab = 16 ; .. a2 + 2ab , or a2 + 2a ( 7 − 2a ) = 16 ; · .. 3a2 – 14a + 16 , or ( 3a - 8 ) ( a− 2 ) = 0 . - Hence the roots are 2 , 2 , 3 . 11. Let the roots be ad , a , and a ...
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A Companion to Wrigley's Collection of Examples: Being Illustrations of ... John Thompson Platts,Alfred Wrigley No preview available - 2016 |
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a+b+c a²+b² a²b³ AB² ABCD AC² angle ABC axis BC² beam centre of gravity chord circle co-ordinates coefficient cos² cos³ cosec² curve diameter draw ellipse equal equilateral Eucl Hence hyperbola Join latus rectum Let ABC middle point MULTINOMIAL THEOREMS parabola parallel perpendicular plane point of contact point of intersection r₁ radius required locus right angle roots S₁ sec² segment sides Similarly sin² sin³ square straight line tan² tangent term transformed equation triangle ABC values vertical weight whence X₁