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
Explanation
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.
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