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Which of the following sets contains all the roots of a polynomial
F(x)=2x^3+x^2-3x
A- {0,1 3/2}
B- {-3/2, 1}
C- {-3/2, 0,1}
D- { -1, -3/2}

Respuesta :

The set that contains all the roots of the polynomial is given by:

C. {-3/2, 0,1}

What are the roots of a polynomial F(x)?

They are the values of x for which F(x) = 0.

In this problem, the polynomial is given by:

F(x) = 2x³ + x² - 3x.

Hence:

2x³ + x² - 3x = 0.

2x(x² + 0.5x - 1.5) = 0.

2x = 0 -> x = 0.

x² + 0.5x - 1.5 = 0 -> (x + 1.5)(x - 1) = 0.

Then, this means that the other two roots are:

  • x + 1.5 = 0 -> x = -1.5.
  • x - 1 = 0 -> x = 1.

Hence the correct option is:

C. {-3/2, 0,1}

More can be learned about the roots of a polynomial at https://brainly.com/question/2833285

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