Question

According to the Fundamental Theorem of Algebra, how many roots exist for the polynomial function?

f(x) = 4x5 – 3x
1 root
2 roots
4 roots
5 roots

Answer 1

Hello,

I say one more time in C there are 5 roots.

`4x^5-3x=x(4x^4-3)\\ =x(2x^2+ √(3) )(2x^2- √(3) )\\ =x( √(2)x- \sqrt[4]{3} ) ( √(2)x+ \sqrt[4]{3} ) ( √(2)x- i\sqrt[4]{3} ) ( √(2)x+i \sqrt[4]{3} )`

Answer 2

Option 4 is correct that is according to fundamental theroem of algebra the given polynomial function will have 5 roots

Explanation:

The fundamental theorem of algebra says that the polynomial will have the number of roots equal to the degree of the polynomial.

Degree is the highest power of polynomial.

Here we have given the polynomial
`4x^5-3x` where degree is 5.

Hence, the given polynomial will have 5 roots.

Therefore, option 4 is correct that is 5 roots