prestongoode00 prestongoode00
  • 23-07-2020
  • Mathematics
contestada

Which of the following sets contains all roots of the polynomial f(x)=2x^3+3x^2-3x-2?

Which of the following sets contains all roots of the polynomial fx2x33x23x2 class=

Respuesta :

jimrgrant1 jimrgrant1
  • 23-07-2020

Answer:

C

Step-by-step explanation:

Given

f(x) = 2x³ + 3x² - 3x - 2

Note that

f(1) = 2 + 3 - 3 - 2 = 0 , thus

(x - 1) is a factor

Dividing f(x) by (x - 1) gives

f(x) = (x - 1)(2x² + 5x + 2) = (x - 1)(x + 2)(2x + 1)

To find the roots equate f(x) to zero, that is

(x - 1)(x + 2)(2x + 1) = 0

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x + 2 = 0 ⇒ x = - 2

2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = - [tex]\frac{1}{2}[/tex]

The solution set is therefore

{ - 2, - [tex]\frac{1}{2}[/tex], 1 } → C

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