 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2021/paper-1/2/solution

Find two numbers with sum

- 1

and product

- 2

: they are

- 2

and

1

. Thus the quadratic polynomial factorizes as

x^{2} - x - 2 = (x - 2) (x + 1) .

The product is negative precisely when its two factors have opposite signs. This occurs between its two polynomial roots, so

- 1 < x < 2.

The endpoints give zero and are excluded by the strict inequality.

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