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**acevipa** How would you approach these questions:

$\displaystyle 1)\ Show\ that\ x^3+x-9=0\ has\ only\ one\ real\ solution.$

Would you differentiate it and then show that the derivative must be greater than 0 for all values of x. Then find a point, which gives a negative value of $\displaystyle f(x)$ and a point that gives a positive value of $\displaystyle f(x)$.

$\displaystyle 2)\ How\ many\ real\ zeros\ does\ p(x)=x^3-12x^2+45x-51\ have?$

Would the answer always be 3. Could there be a case, where it is not 3.