Respuesta :
We have the polynomial:
[tex]4x^3-6x^2+9x+10[/tex]We have to find the roots of this polynomial, using the rational root theorem.
This theorem tells us that, for this polynomial to have a rational root, the leading coefficient must be divisible by the denominator of the root fraction, and the constant term (the one that is not multiplying x) has to be divisible by the root numerator.
Then, if we look at the first condition, the root 1/3 (option F) is not a feasible solution.
All the others have numerators for which the leading coefficient (4) is divisible.
When we look at the second condition, the possible divisors of 10 are: 2, 5 and 10.
Then, the root 6 (option C) is not a feasible solution.
Option A (root x=-2), Option B (root 5), Option D (root 5/4) and Option E (root -1/2) satisfy both conditions, so they can be roots of the polynomial.
The options that does not satisfy the conditions are C and F.
