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

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 = -

The solution set is therefore

{ - 2, - , 1 } → C

the nearest power is 1.651.

means 7482 to the 1.651th power is almost equal to 2489287

in simplified version   it would be x ≤-4

step-by-step explanation:

multiply each term in x ≤-4 by -1