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( URGENT) What are the roots of the polynomial equation x Superscript 4 Baseline + x cubed = 4 x squared + 4 x? Use a graphing calculator and a system of equations.
–2, –1, 0, 2
–2, 0, 1, 2
–1, 0
0, 1

Respuesta :

Answer:

A.

Step-by-step explanation:

MrRoyal

The roots of the polynomial equation are (a) –2, –1, 0, 2

How to determine the roots?

The polynomial equation is given as:

[tex]x^4 + x^3 = 4x^2 + 4x[/tex]

Rewrite as:

[tex]x^4 + x^3 - 4x^2 - 4x = 0[/tex]

Factorize

[tex]x(x^3 + x^2 - 4x - 4) = 0[/tex]

This means that:

x = 0 and [tex]x^3 + x^2 - 4x - 4 = 0[/tex]

Factorize

[tex]x^2(x + 1) - 4(x + 1) = 0[/tex]

Factor out x + 1

[tex](x^2 - 4)(x + 1) = 0[/tex]

Express as difference of two squares

[tex](x - 2)(x + 2)(x + 1) = 0[/tex]

This means that:

x = 2, -2 and -1

Hence, the roots of the polynomial equation are (a) –2, –1, 0, 2

Read more about polynomials at:

https://brainly.com/question/11536910

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