Polynomial:
$$(8.0\times10^{29})(0.010-x)(1.99\times10^{-7}-4x)^4-x=0.$$
No matter what I do can't get the graph to show up on my calculator (TI-83 plus) when I use the graphing function, so I can't use it to find the zeroes in order to solve for x. I am a total math novice and am in general chemistry (not a math student) so please be kind and assume I don't know anything! Is there another way to solve for x on my calculator besides graphing?
Thanks!
You can ignore the $x$ term at the right as it is tiny compared to everything else. The leading factor of $8.0 \cdot 10^{29}$ makes sure of it. The largest term in $x$ that comes from expanding the product is $8.0 \cdot 10^{29}\cdot 0.010 \cdot 4 \cdot (1.99 \cdot 10^{-7})^3 \cdot -4\approx -1.0\cdot 10^9$, so changing that by $1$ makes no difference. Then you can see the roots are $0.010$ and a quadruple root at $\frac 14\cdot 1.99\cdot 10^{-7}\approx 5.0\cdot 10^{-8}$