 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/1/solution

Bring all terms to the left and factor the quadratic polynomial:

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

Its leading coefficient is positive, so it is nonpositive between its two polynomial roots, including the endpoints. Therefore

- 2 \leq x \leq \frac{3}{2} .

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