Hey guys. I'm having trouble with this problem.
Find all of the zeros of the following polynomial and give them in a comma-separated list. If there are no zeros, enter None .
Note: complex numbers should be in the form (a+bi).
Hey guys. I'm having trouble with this problem.
Find all of the zeros of the following polynomial and give them in a comma-separated list. If there are no zeros, enter None .
Note: complex numbers should be in the form (a+bi).
First thing you should not is that when x=1, the function is equal to 0.
Using long division, you can find that:
$\displaystyle x^4+4x^3-3x^2+8x-10 = (x-1)(x^3+5x^2+2x+10)$
Note that when $\displaystyle x=-5$ , $\displaystyle (x^3+5x^2+2x+10)=0$
Using long division, you can find that:
$\displaystyle (x^3+5x^2+2x+10) = (x+5)(x^2+2)$
So we have that:
$\displaystyle x^4+4x^3-3x^2+8x-10 = (x-1)(x+5)(x^2+2)$
Now just find the values of x that make this expression equal to 0.