. Differential and integral calculus, an introductory course for colleges and engineering schools. + and — signs within that interval. In other words, if f(xi) = 0,we cannot assert that f(x) changes sign at Xi = 0, or that thegraph crosses OX at X\. For plainly the graph may have one ofthe forms shown in the figures. To ascertain in such a casewhether f{x) does actually change sign, we have only to deter-mine the signs of f(x\— h) and f(xi+ h) for a sufficiently smallvalue of h. 51. Roots of Polynomials. A root of a polynomial is any valueof the argument which makes the polynomial zero. The ro
. Differential and integral calculus, an introductory course for colleges and engineering schools. + and — signs within that interval. In other words, if f(xi) = 0,we cannot assert that f(x) changes sign at Xi = 0, or that thegraph crosses OX at X\. For plainly the graph may have one ofthe forms shown in the figures. To ascertain in such a casewhether f{x) does actually change sign, we have only to deter-mine the signs of f(x\— h) and f(xi+ h) for a sufficiently smallvalue of h. 51. Roots of Polynomials. A root of a polynomial is any valueof the argument which makes the polynomial zero. The rootsmay be real or complex. An equivalent geometrical definitionfor a real root is the following: A real root of a polynomial is the abscissa of a point in whichthe graph of the polynomial cuts the rr-axis. An algebraic equation is a polynomial put equal to zero, and aroot of such an equation is any value of the argument which satis-fies it. Plainly, a root of an equation is the same thing as a rootof the polynomial which constitutes the first member of theequation. Examples. 1. 1 and 2 are
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