SOLUTION: Use the Intermediate Value Theorem to determine if P(x) = 2x^5 - 7x +1 has a zero in the intervals [1,2].

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Intermediate Value Theorem to determine if P(x) = 2x^5 - 7x +1 has a zero in the intervals [1,2].      Log On


   

Question 90245: Use the Intermediate Value Theorem to determine if P(x) = 2x^5 - 7x +1 has a zero in the intervals [1,2].
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's evaluate f%281%29

f%28x%29=2x%5E5-7x%2B1 Start with the given polynomial


f%281%29=2%281%29%5E5-7%281%29%2B1 Plug in x=1


f%281%29=2%281%29-7%281%29%2B1 Raise 1 to the fifth power to get 1


f%281%29=2-7%281%29%2B1 Multiply 2 by 1 to get 2


f%281%29=2-7%2B1 Multiply 7 by 1 to get 7


f%281%29=-4 Now combine like terms




Now let's evaluate f%282%29



f%28x%29=2x%5E5-7x%2B1 Start with the given polynomial


f%282%29=2%282%29%5E5-7%282%29%2B1 Plug in x=2


f%282%29=2%2832%29-7%282%29%2B1 Raise 2 to the fifth power to get 32


f%282%29=64-7%282%29%2B1 Multiply 2 by 32 to get 64


f%282%29=64-14%2B1 Multiply 7 by 2 to get 14


f%282%29=51 Now combine like terms

Since our y-value changes from a negative value to a positive value in the interval [1,2] this means there is a zero in this interval.