. Differential and integral calculus, an introductory course for colleges and engineering schools. 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 al
. Differential and integral calculus, an introductory course for colleges and engineering schools. 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 roots of the polynomial x2stituted for x they make the polynomialzero. Also, 1 and 2 are roots of the alge-braic equation x2- 3x+2= 0. The graph of the polynomial is shown inthe figure. 3 x + 2, because when sub-. 66 DIFFERENTIAL CALCULUS §51 2. The roots of the polynomial x2—3x+3 are 3±V-3 because \F
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