taiwan-gsat 2022 Q4

taiwan-gsat · Other · ast__math-a 8 marks Polynomial Division & Manipulation

Let the polynomials $f(x) = x^3 + 2x^2 - 2x + k$ and $g(x) = x^2 + ax + 1$, where $k, a$ are real numbers. Given that $g(x)$ divides $f(x)$ and the equation $g(x) = 0$ has complex roots, select the option that is a root of the equation $f(x) = 0$.
(1) $-3$
(2) $0$
(3) $1$
(4) $\frac{1 + \sqrt{-3}}{2}$
(5) $\frac{3 + \sqrt{-5}}{2}$

Let the polynomials $f(x) = x^3 + 2x^2 - 2x + k$ and $g(x) = x^2 + ax + 1$, where $k, a$ are real numbers. Given that $g(x)$ divides $f(x)$ and the equation $g(x) = 0$ has complex roots, select the option that is a root of the equation $f(x) = 0$.\\
(1) $-3$\\
(2) $0$\\
(3) $1$\\
(4) $\frac{1 + \sqrt{-3}}{2}$\\
(5) $\frac{3 + \sqrt{-5}}{2}$

Paper Questions

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