use the intermediate value theoremto show that the polynomial function has a zero in the given interval

f(x)=x^5-x^4+8x^3-5x^2-14x5;[1.4;1.5]

find the value of f (1.4)=
find the value of f (1.5)=

show work, thanks

A visit to the bottom of the page at

http://rechneronline.de/function-graphs/

will allow you to enter your function and a list of values to evaluate.

Since you left out a + or - sign in 14x5, I'll not evaluate f(x), but you will surely find that f(1.4) and f(1.5) have opposite signs. So, the IVT says that there is a root in the interval.