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Use the fundamental theorem of algebra to determine the number of roots for each polynomial function shown.

1.) f (x) = 2x3 + x2 - 7x + 1 has ___ roots.

2.) f (x) = -3x + 5x2 + 8 has ___ roots.

3.) f (x) = (x2 + 6)2 has ___ roots.

Respuesta :

1.) f (x) = 2x3 + x2 - 7x + 1 has 3 roots.

2.) f (x) = -3x + 5x2 + 8 has 2  roots.

3.) f (x) = (x2 + 6)2 has 4 roots.
aksnkj

Answer:

The first polynomial will have 3 roots, second will have 2 roots and third will have 4 roots.

Step-by-step explanation:

Fundamental theorem of algebra says that for each polynomial of degree n, there exists n number of roots.

From the given polynomial, find the degree of the polynomial and then predict the number of root it can have.

Degree of the polynomial is the highest power of the variable.

(1). The given polynomial is [tex]f (x) = 2x^3 + x^2 - 7x + 1[/tex].

The highest power of the variable or degree of the polynomial is 3. Thus, it will have 3 roots.

(2). The given polynomial is

[tex]f (x) = -3x + 5x^2 + 8 \\f(x)=5x^2 -3x+ 8[/tex]

The highest power of the variable or degree of the polynomial is 2. Thus, it will have 2 roots.

(3). The given polynomial is

[tex]f (x) = (x^2 + 6)^2\\f(x)=x^4+12x^2+36[/tex]

The highest power of the variable or degree of the polynomial is 4. Thus, it will have 4 roots.

Therefore, first polynomial will have 3 roots, second will have 2 roots and third will have 4 roots.

For more details, refer the link:

https://brainly.com/question/2770908?referrer=searchResults

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