Wikipedia:Reference desk/Archives/Mathematics/2017 March 12
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March 12
editFormula for product of x-intercepts (if all real numbers) of a polynomial
editIs 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)
- Count Iblis (talk) 20:06, 12 March 2017 (UTC)
- @Georgia guy: 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)