my solution:kaliprasad said:if for rational a,b,c $ax^3+bx+c=0$ one root is product of 2 roots then that root is rational
A rational root is a number that can be expressed as a ratio of two integers, such as 1/2, -3/4, or 5/6.
To determine if a polynomial has rational roots, you can use the rational root theorem. This theorem states that if a polynomial has rational roots, they will be in the form of p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
To find the rational roots of a polynomial, you can use the rational root theorem as well as the synthetic division method. First, list all possible rational roots by taking the factors of the constant term and dividing them by the factors of the leading coefficient. Then, use synthetic division to test each root until you find one that gives a remainder of 0.
If the rational root of a polynomial is a product of two rational roots, it means that the polynomial can be factored into two linear factors, each with a rational root. This can help simplify the polynomial and make it easier to solve.
Yes, a polynomial can have more than one rational root. In fact, if a polynomial has a rational root, it will have at least one more rational root. This is because if p/q is a root, then (x-p/q) will be a factor of the polynomial, and the remaining factor will have a rational root as well.