Question 1192628
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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.
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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;At this point, &nbsp;all explanations are completed.


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On solving quadratic equations using the quadratic formula, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Introduction-Into-Quadratics.lesson>Introduction into Quadratic Equations</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/proof-of-quadratic-by-completing-the-square.lesson>PROOF of quadratic formula by completing the square</A>

in this site.