Wikipedia:Reference desk/Archives/Mathematics/2017 March 12

= March 12 =

Formula for product of x-intercepts (if all real numbers) of a polynomial
Is there any formula for the product of all x-intercepts of a polynomial?? A linear polynomial always has -b/m as its sole x-intercept. A quadratic polynomial with 2 x-intercepts will have them multiply to -c/a. Is there any formula for the product of all x-intercepts of any polynomial?? Georgia guy (talk) 19:49, 12 March 2017 (UTC)


 * $$A\prod_{j=1}^{n}(x-\alpha_j)= A x^n+\cdots +(-1)^n A\prod_{j=1}^n\alpha_j$$ Count Iblis (talk) 20:06, 12 March 2017 (UTC)
 * More generally, see Vieta's formulas. The product of the roots is always equal to the quotient of the coefficient of the constant term by the coefficient of the highest-order nonzero term, times -1 raised to the power of the degree of the polynomial.
 * This includes complex roots as well. In general, there is no easy way to remove the complex roots from the product and still have a clean formula in terms of the coefficients.--Jasper Deng (talk) 20:11, 12 March 2017 (UTC)