If p(x) is a polynomial such that P(1) = -1 and P(2) = 3, must p(x) = 0 have a rational root between x =1 and x = 2? Justify your answer.
-
Not necessary rational root but a real root.
The reasoning for this is that the y value at x = 1 is negative and the y value at x = 2 is positive. Therefore, if the graph is continuous between the interval [1,2], then the curve actually crosses the x-axis and therefore must have a real root in the said interval.
The reasoning for this is that the y value at x = 1 is negative and the y value at x = 2 is positive. Therefore, if the graph is continuous between the interval [1,2], then the curve actually crosses the x-axis and therefore must have a real root in the said interval.