SOLUTION: Here is another one..I am stumped as to what to do!! Help please!! I need steps to understand this. Use the intermediate value theorem to show that the polynomial function has a

Algebra ->  Rational-functions -> SOLUTION: Here is another one..I am stumped as to what to do!! Help please!! I need steps to understand this. Use the intermediate value theorem to show that the polynomial function has a      Log On


   

Question 970034: Here is another one..I am stumped as to what to do!! Help please!! I need steps to understand this.
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=x^5-x^4+5x^3-4x^2-20x+18: [1.5,1.9]
Thank you in advance!!!
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=x%5E5-x%5E4%2B5x%5E3-4x%5E2-20x%2B18: interval:[1.5,1.9]
if x=1.5,
f%281.5%29=%281.5%29%5E5-%281.5%29%5E4%2B5%281.5%29%5E3-4%281.5%29%5E2-20%281.5%29%2B18
f%281.5%29=-1.59375
if x=1.9,
f%281.9%29=%281.9%29%5E5-%281.9%29%5E4%2B5%281.9%29%5E3-4%281.9%29%5E2-20%281.9%29%2B18
f%281.9%29=11.58389
Now we know:
at x=1.5, the curve is below zero
at x=1.9, the curve is above zero
And, being a polynomial, the curve will be continuous.
So, somewhere in between, the curve must cross through y=0


zero is at x=1.59204 and 1.5%3C1.59204%3C1.9