Final answer:
The equation 3x⁴−8x³+2=0 has a solution in the interval [2,3] due to the intermediate value theorem.
Step-by-step explanation:
To show that the equation 3x⁴−8x³+2=0 has a solution in the interval [2,3], we can use the intermediate value theorem. The intermediate value theorem states that if a continuous function f(x) changes sign over an interval [a, b], then there exists at least one value c in the interval (a, b) where f(c) = 0. In this case, the polynomial function 3x⁴−8x³+2 is continuous, and it changes sign from positive to negative within the interval [2,3]. Therefore, we can conclude that there is at least one solution to the equation in the interval [2,3].