Find zeros of f(x)=x4−5x3+10x2−20x+24?
Find zeros of f(x)=x^4−5x^3+10x^2−20x+24 then write it in the factored form, including complex roots.
I have tried everything can some one explain this to me D:....it just wont factor....and synthetic division didn't work to find a zero.
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f(3) = 0 (i discovered it by trial and error) (note typically the number that leads to a zero is a factor of the constant in this case 24 which is 3*8)
with the long division of your equation with x-3 yields x3 -2x2 +4x -8
lets call g(x) x3 -2x2 +4x -8
now finding a zero in this new equation is easier and it will still lead to the zeros in the original equation g(2) = 0 (again by trial and error)
this implies that f(2) = 0
with the long division of x3 -2x2 +4x -8 with x-2 yields x2 +4
from here use the formula to obtain the complex roots
which are
4i and - 4i
concluding: the 4 roots of this polinomial are 2, 3, 4i and -4i