 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2018/paper-1/2/a/solution

Move the constant term to the left and factor the cubic polynomial:

2 x^{3} + 9 x^{2} - 6 x - 5 = (x - 1) (2 x + 1) (x + 5) .

Setting each factor to zero gives all three polynomial roots:

x = 1, - \frac{1}{2}, - 5.

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