If -1 is the root of 4x³ - x² - 11x - 6 = 0 then other roots are _____?
Maths / Algebra MCQs — Multiple-choice practice
- A. 3, 3/4
- B. None of these
- C. 2, -3/4
- D. 1, 3/4
Correct answer
2, -3/4
Explanation
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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