All the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 are x = -2, x = -0.5, x = 0, x = 2 ( Option A ).
Given polynomial :
2x⁴+ x³-8x²- 4x = 0
The highest power of the polynomial is 4. This implies that this polynomial will have 4 roots or 4 zeroes.
There are numerous ways of finding roots or zeroes of a polynomial of any degree.
A root or zero of a polynomial is a solution or value of the variable which gives the value of the polynomial equal to 0.
Since this is a multiple choice based question, the easiest approach to this question is by eliminating options and finding the correct answer.
Option B and C get eliminated instantly because they have only three roots, however this is a polynomial of degree 4 and should have 4 roots.
For option A and C, we put x= -2, x = -0.5, x = 0, x = 2, and x = 0.5 in the given polynomial to check if the answer is equal to zero.
For x = -2, we get 2x⁴+ x³-8x²- 4x = 0
For x = 2, we get 2x⁴+ x³-8x²- 4x = 0
For x = 0, we get 2x⁴+ x³-8x²- 4x = 0
For x = -0.5, we get 2x⁴+ x³-8x²- 4x = 0
For x = 0.5, we get 2x⁴+ x³-8x²- 4x = -3.75
From this result, option C gets ruled out and all the values in option A check out as a root of the given polynomial.
Therefore, we get all the roots of the polynomial 2x⁴+ x³-8x²- 4x = 0 as x = -2, x = -0.5, x = 0, x = 2
Learn more about Polynomials here:
https://brainly.com/question/11536910?referrer=searchResults
#SPJ9
