Question

Determine the zeros of f(x) = x4 – x3 + 7x2 – 9x – 18.
help :))

Answer 1

x=-1,2

Answer 2

cheat

Answer 3

find them instantly, since you are already on line, just type it in
http://www.wolframalpha.com/input/?i=x4+%E2%80%93+x3+%2B+7x2+%E2%80%93+9x+%E2%80%93+18.

Answer 4

how did you get tht DASHNI?

Answer 5

We'll have to substitute and check . Let's put x=-1
f(-1)=1+1+7+9-18=0
so x+1 is a factor, we'll create this factor and will find other factors
f(x)=x^4-x^3+7x^2-9x-18
writing x^4 as x^3(x+1) this has added an extra x^3, so will subtract this by -x^3
x^4---->x^3(x+1)-x^3
so creating this factor in each term
f(x)=x^3(x+1)-2x^2(x+1)+9x(x+1)-18x-18
f(x)=x^3(x+1)-2x^2(x+1)+9x(x+1)-18(x+1)
f(x)=(x+1)(x^3-2x^2+9x-18)

Answer 6

now we'll find factors of (x^3-2x^2+9x-18)
let's check if x=-1 is a factor of this
-1-2-9-18 =-30 not equal to zero, let's check if x=2 is a factor
8-8+18-18=0
so x-2 is a factor
now we'll create this factor in each term, like done before
x^2(x-2)+9(x-2)
(x-2)(x^2+9)
so f(x)= (x+1)(x-2) (x^2+9)
so the two real roots are x=-1, 2
the complex roots are
\[x= \pm 3i\]

Answer 7

thank you very much:)

Answer 8

welcome:)