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(52769)   (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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