find the zeroes of the polynomial x^3-4x
Answers
Given :
Given :To find the zeroes of the polynomial
x³-4x
SOLUTION :
TO find the zeroes of the polynomial, we need an equation or equality ....
FOR EXAMPLE.....
x³-4x=0
HERE THERE IS NO EQUALITY EXIST, HENCE THERE IS NO ZEROES EXIST FOR IT....
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#ANSWER WITH QUALITY......
Answer:
Step-by-step explanation:
First, we need to find one factor of the polynomial and then divide it so that we get another factor. After getting the other factor, we can factorize that to get two more factors. So we can find totally, 3 factors.
We will use factor theorem.
x^3-4x=0 is the equation given.
Let x=1
1^3-4*1=1-4=-3, not equal to 0. Therefore, x-1 is not a factor.
Let x=-1
-1^3-4*-1=-1+4=3, not equal to 0. Therefore, x+1 is not a factor.
Let x=2
2^3-4*2=8-8=0
Therefore, x-2 IS A FACTOR OF x^3-4x.
Dividing x^3-4x by x-2, we get x^2+2x as quotient and remainder would be 0 of course since x-2 is a factor of the given polynomial.
x^2+2x= x(x+2).
Therefore, x+2, x-2, x are the FACTORS of the polynomial x^3-4x.
Therefore, -2, 2, 0 are the zeroes of the given polynomial.