If -1 is the root of 4x³ - x² - 11x - 6 = 0 then other roots are _____?

2, -3/4

3, 3/4

1, 3/4

None of these

Given the equation 4x³ - x² - 11x - 6 = 0 and -1 is a root:

Step 1: Factor out the known root

If -1 is a root, (x + 1) is a factor. Perform polynomial division:

4x³ - x² - 11x - 6 = (x + 1)(4x² - 5x - 6)

Step 2: Factor the quadratic equation

4x² - 5x - 6 = (4x + 3)(x - 2)

Step 3: Find the roots

The factors are (x + 1)(4x + 3)(x - 2) = 0

Roots are x = -1, x = -3/4, and x = 2

The other roots are 2 and -3/4.