2 янв. 2019 г. · In p(x)=x3−x2, both 0 and 1 are possible roots of the polynomial; both are real. I had read that a cubic polynomial has either all real roots or ...

24 мая 2021 г. · p′(x) cannot have two distinct roots between consecutive roots of p(x), if p(x) is a cubic polynomial with real coefficients.

28 янв. 2020 г. · Two different double roots would mean 4 roots, and a cubic has only three roots. So the answer is no.

16 мая 2013 г. · A cubic has 3 real roots if and only if it has a local minimum and a local maximum and the product of those two values is ≤0.

18 янв. 2018 г. · I am not sure how to go about the following problem: Find the cubic polynomial function with two of its zeros: 2 and (-3+sqrt2) , and a y-intercept of 7.

2 февр. 2014 г. · Yes, if you count roots geometrically. You can have a cubic polynomial with only two rational numbers as roots. e.g. (x−1) ...

26 сент. 2017 г. · A cubic equation has at least one real root this can be shown using the Intermediate Value Theorem.

10 дек. 2016 г. · the derivative of a cubic is a quadratic, which can have either 2 or 0 real roots, never 1; look at cubics which have both a local maximum and ...

15 дек. 2013 г. · As a polynomial has a number of zeroes equals to its degree, a cubic has at least one real root. Just take the first and second derivatives and ...

10 мар. 2019 г. · A cubic with real coefficients always has at least one real root, so there is no counterexample of a cubic with real coefficients with no real roots.