 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2023/paper-1/2/solution

The given polynomial root supplies the factor

2 x - 3

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

Solving the remaining quadratic equation, the other two polynomial roots are

x = \frac{1 + 5}{2} and x = \frac{1 - 5}{2} .

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