Thread: Root Linear Coefficient Theorem

Hi Forum (I'm new)

Root Linear Coefficient Theorem: "The sum of the reciprocal of the roots of a polynomial equals the negative of the coefficient of the linear term in the Maclaurin series" (Root Linear Coefficient Theorem -- from Wolfram MathWorld)

I get it equals the negative of the ratio of the linear coefficient to the constant term.

where and I'm using Vieta's Formulas (Vieta's Formulas)

I'm pretty sure that's right... What went wrong?

I believe that you require the polynomial itself is monic, i.e., the leading coefficient is 1; otherwise, "the negative of the coeff. of the linear term" may not even be defined. For instance, f(x)=x^2-3x and g(x)=2x^2-6x, both have precisely the same roots, but the coefficients of x are definitely distinct.

Hope this helps.

Thanks for answering. If the constant term is non-zero, can I assume the sum is then?

Originally Posted by sleepingcat

Thanks for answering. If the constant term is non-zero, can I assume the sum is then?

Yes