Moderate -0.8 This is a straightforward recall question testing the fundamental property that complex roots of polynomials with real coefficients come in conjugate pairs. Since 5i is a root, -5i must also be a root, giving factor (x-5i)(x+5i) = x²+25. Requires only one conceptual step with no calculation or problem-solving.
The function f is a quartic function with real coefficients.
The complex number \(5i\) is a root of the equation \(f(x) = 0\)
Which one of the following must be a factor of \(f(x)\)?
Circle your answer.
[1 mark]
\((x^2 - 25)\) \quad\quad \((x^2 - 5)\) \quad\quad \((x^2 + 5)\) \quad\quad \((x^2 + 25)\)
The function f is a quartic function with real coefficients.
The complex number $5i$ is a root of the equation $f(x) = 0$
Which one of the following must be a factor of $f(x)$?
Circle your answer.
[1 mark]
$(x^2 - 25)$ \quad\quad $(x^2 - 5)$ \quad\quad $(x^2 + 5)$ \quad\quad $(x^2 + 25)$
\hfill \mbox{\textit{AQA Further Paper 2 2024 Q4 [1]}}