Answer:
±5/2
Explanation:
The rational root theorem states that any rational root of a polynomial with integer coefficients must be of the form p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
For the polynomial 4x^3 + 9x^2 - x + 10, the constant term is 10 and the leading coefficient is 4. Therefore, any rational root must be of the form p/q, where p is a factor of 10 and q is a factor of 4.
The factors of 10 are 1, 2, 5, and 10, and the factors of 4 are 1, 2, and 4. So the possible rational roots are:
p/q = ±1/1, ±2/1, ±5/1, ±10/1, ±1/2, [±5/2]