A Treatise On the Nature And Properties of Algebraic Equations
A Treatise On the Nature And Properties of Algebraic Equations
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To quickly assess the difficulty of the text, read a short excerpt:
Thus, to render the coefficients of the equation integers, we must assume m = 2 . 3 = 6, and the resulting equation will be y 3 + I2y 2 + 9y + 24 = 0.
This transformation might also be effected by elimination, as follows : /(*) = o, y = mx.
Hence x = -, m and/g) = 0.
TRANSFORMATION OF EQUATIONS. 31 Ex. 4. To find the equation whose roots are the squares of the roots of the given equation.
Here we have to eliminate x from the equations /(*) = o, y == z 2 ; and the result is to be an equation in ...y, not containing frac- tional powers of y ; which it must do if the elimination were performed by substituting for x its values ± s/y.
Instead then of this elimination, we shall form a polyno- mial of the 2n th degree, and containing only even powers of x; the form of the polynomial being the product of the factors (a-a _ a 2 ) (x 2 — b 2 ) (x 2 — c 2 ) .... (z 2 — I 2 ) ; and then write y for x 2, and equate to zero.
Now, observing that we have /(*) = Cf - a) (x - b) (*-/), /(- *> = (- l)», (i + a)
What to read after A Treatise On the Nature And Properties of Algebraic Equations?
You can find similar books in the "Read Also" column, or choose other free books by Robert Stevenson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Thus, to render the coefficients of the equation integers, we must assume m = 2 . 3 = 6, and the resulting equation will be y 3 + I2y 2 + 9y + 24 = 0.
This transformation might also be effected by elimination, as follows : /(*) = o, y = mx.
Hence x = -, m and/g) = 0.
TRANSFORMATION OF EQUATIONS. 31 Ex. 4. To find the equation whose roots are the squares of the roots of the given equation.
Here we have to eliminate x from the equations /(*) = o, y == z 2 ; and the result is to be an equation in ...y, not containing frac- tional powers of y ; which it must do if the elimination were performed by substituting for x its values ± s/y.
Instead then of this elimination, we shall form a polyno- mial of the 2n th degree, and containing only even powers of x; the form of the polynomial being the product of the factors (a-a _ a 2 ) (x 2 — b 2 ) (x 2 — c 2 ) .... (z 2 — I 2 ) ; and then write y for x 2, and equate to zero.
Now, observing that we have /(*) = Cf - a) (x - b) (*-/), /(- *> = (- l)», (i + a)
What to read after A Treatise On the Nature And Properties of Algebraic Equations?
You can find similar books in the "Read Also" column, or choose other free books by Robert Stevenson to read onlineMoreLess
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