Well, try
to find the solution for this…
-0.2x⁵ + 0.04x⁴ - 0.0625x³ - 2x² + 0.3x + 4=0
<span>The answer
is 1.33. How would you figure it out without a computer?
In order to find all the roots of a polynome with a grade lower than 2, we need
to know at least 1 root (this polynome has grade 5). We can try with the
divisors of the constant (4 is the constant), which are: 1,-1,2,-2,4 and -4.
But no, none of them verifies the equation! So it will be of hard to find a
root. That’s because there are too many fractions, and a fraction can come from
a variety of divisions. It’s even more difficult to find a root when there are
irrational numbers among the roots (such as the square root of 2, or half a pi,
or e). So, if we don’t know any of the roots, we can’t work with the Ruffini
rule.</span>
So in this
case I suggest to put this in a graphic software:
y=-0.2x⁵ + 0.04x⁴ - 0.0625x³ - 2x² + 0.3x + 4
And there
you have the plot. Then you click in “roots” and it will tell you the point: (1.33,0).
So that’s how you know 1.33 is the answer.
