SOLUTION: Use the intermediate value theorem to show that the function has a real zero between the two numbers given.​ Then, use your calculator to approximate the zero. p(x)=4x^2-2x-6; 1

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Question 1192628: Use the intermediate value theorem to show that the function has a real zero between the two numbers given.​ Then, use your calculator to approximate the zero.
p(x)=4x^2-2x-6; 1 and 2
p(1)=
p(2)=
Is there a zero between 1 and​ 2? (y/n)
The zero is approximately=
​(Round to the nearest hundredth as​ needed.)
thank you, still trying to grasp how to do this im clueless
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

To answer first question, you need to calculate the values p(1) and p(2).


To calculate p(1), substitute x= 1 into the formula.

To calculate p(2), substitute x= 2 into the formula.


If the values p(1) and p(2) are of different signs (of opposite signs), then 

the intermediate value theorem says that there is a root  p(x) = 0 somewhere in the interval (1,2).



At this point,  explanation to the first question is complete.



Regarding your second question, solve the quadratic equation

    4x^2-2x-6 = 0 


using the quadratic formula, the calculate the roots using your calculator.


                At this point,  all explanations are completed.

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On solving quadratic equations using the quadratic formula,  see the lessons
    - Introduction into Quadratic Equations
    - PROOF of quadratic formula by completing the square
in this site.



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