SOLUTION: Use the intermediate value theorem to show that the function has a zero between the two numbers given.​ Then, use your calculator to approximate the zero to the nearest hundredth

Algebra ->  Equations -> SOLUTION: Use the intermediate value theorem to show that the function has a zero between the two numbers given.​ Then, use your calculator to approximate the zero to the nearest hundredth      Log On


   

Question 1192454: Use the intermediate value theorem to show that the function has a zero between the two numbers given.​ Then, use your calculator to approximate the zero to the nearest hundredth.
P(x)=6x^4-6x^2+4x-2;0.5 and 1
Any help is appreciated thank you!
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Plug in x = 0.5
P(x)=6x^4-6x^2+4x-2
P(0.5)=6(0.5)^4-6(0.5)^2+4(0.5)-2
P(0.5)=-1.125
The result is negative.

Repeat for x = 1
P(x)=6x^4-6x^2+4x-2
P(1)=6(1)^4-6(1)^2+4(1)-2
P(1)=2
The result is positive.

The actual numeric values don't matter.
All we care about are the signs of the results.

The value of P(0.5) is negative and P(1) is positive.

The transition from negative to positive means that somewhere along the line is at least one x intercept or root.
This is because the curve is continuous meaning there aren't any gaps or jumps.
Any polynomial is continuous.

Using a graphing calculator like desmos or geogebra would show that the root on this interval is roughly x = 0.83