Question

Find all the roots or zeros for the following polynomial. f(x)= x^4 - 2x^3 + 5x^2 - 8x + 4

Answer 1

what is the sum of all co-efficients ?

Answer 2

1 -2 +5 -8 +4 = 0

Answer 3

?

Answer 4

yes, does that suggest anything to you ?
sum of all co-efficients = 0
then x= ??? is the root.

Answer 5

x=0 can i use synthetic division for this ?

Answer 6

everything = 0 ?

Answer 7

not x=0
x=1
put x=1 in your equation to verify...

Answer 8

and yes, then you use synthetic division
know how to ?

Answer 9

i know how to use synthetic division. am i using 1 to divde all the coefficents?

Answer 10

no,
we concluded x=1 is a root
i was just saying that you can verify it by putting x=1 in f(x), you get f(1)=0

Answer 11

and since you know synthetic, do it taking x=1

Answer 12

that is my set up?

Answer 13

yes, correct