Use a graphing device to find all real solutions of the equation $x^5 + 2.00 x^4 + 0.96x^3 + 5.00x^2 + 10.00 x + 4.80 = 0 $
Let $P(x) = x^5 + 2.00 x^4 + 0.96x^3 + 5.00x^2 + 10.00 x + 4.80$
To choose a viewing rectangle that is certain to contain all the $x$-intercepts of $P$, we use the upper and lower bounds theorem to find two numbers between which all the solutions must lie. We use synthetic division and proceed by trial and error.
To find an upper bound, we try the numbers $1,2,3,4,....$
We see that $1$ is the lower bound.
Now we look for the lower bound, trying the numbers $-1,-2,-3,-4,....$
We see that $-3$ is a lower bound,
Thus all the solutions lie between $-3$ and $1$. So the viewing rectangle $[-3,1]$ by $[-10,10]$ contains all the $x$-intercepts of $P$
Based from the graph, we find that the real solutions of the equation are $-1.7, -1.2$ and $-1.8$.
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