Page:Elementary algebra (1896).djvu/512

494 Rh 1 -3 -2 +5 1.2016 1 -2 -4 -2 -4 (A) 1 1 -1 -.992 -1 (A) -5 (B) ,008 1 .04 - .004879399 (A) 0 - 4.96 (C) 008120601 2 08 2(iB) -4.88 2 .000601 4 - 4.879399 2 .000602 (B).6 (C) - 4.878797 .001 .601 .001 .602 .001 (C) .603

We may now state the rule for finding the approximate value of a positive incommensurable root by Horner’s Method.

Rule. Find the integral part of the root by Sturm’s Theorem or method of Art. 602.

Transform the equation into another, each of whose roots shall be less by the integral part of the root.

If in this transformed equation the coefficient of the first power of the unknown quantity and the last term have the same sign, another figure of the root should be found by the method used to find the integral part of the root. If, however, the signs of these terms are unlike, divide the latter by the former, and the first figure of the quotient will be, approximately, the next figure of the root.

Transform the last equation into another whose roots shall be less by this approximate figure of the root found by division, and proceed as before to find another figure of the root.