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VI.—Least Roots of Equations

Published online by Cambridge University Press:  14 March 2016

J. Douglas Hamilton Dickson
J. Douglas Hamilton Dickson*
Affiliation:
St Peter's College, Cambridge
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Extract

(I.) Let F(x) = 10 + b1x + … + bnxn = 0 be an equation whose roots are all real and different; then

where ϕ(x) = 1 + a1x + … + amxm and Σ indicates summation for all the roots of F(x) = 0: of which r is a root.

Let also

then

and equating coefficients of like power of x,

whence

the suffix number indicating the order of the determinant.

Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 28 , Issue 1 , 1877 , pp. 119 - 133
Copyright
Copyright © Royal Society of Edinburgh 1876

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