A2 June 2024 Paper 2 Q4

4 The function \(\mathrm{f}\) is a quartic function with real coefficients.

The complex number \(5\mathrm{i}\) is a root of the equation \(\mathrm{f}(x) = 0\)

Which one of the following must be a factor of \(\mathrm{f}(x)\)?

Circle your answer. [1 mark]

• \((x^2 - 25)\)
• \((x^2 - 5)\)
• \((x^2 + 5)\)
• \((x^2 + 25)\)