using the intermediate value theorem determine if possible w

using the intermediate value theorem, determine, if possible, whether the given function has at least one real zero between a and b.

Solution

Solution:-Given that f(x)=x⁴-14x²+33 and also given that a=-2 and b=-1

f(-2)=(-2)⁴-14(-2)²+33

=-7

and f(-1) =(-1)⁴-14(-1)²+33

-13+33=20

the values of f(-2) to f(-1) gives negative to positive values.

The given fuction is polynomial function,so the function is continuous in the interval [-2,-1].

Also,the value of f(a)=f(-1)=-7 and the value of f(b)=f(-1)=20

So the values changes from negative to positive.Hence by Intermediate value theorem,there exist a real zero lies between a and b.

If we plot a graph between these two,there exist atleast one real zero between -2 to -1.

So by intermediate value theorem,there exist a real zero between -2 and -1