Moderate -0.3 This is a straightforward application of Vieta's formulas combined with polynomial substitution. Students need to recognize that evaluating the polynomial at x = -2 gives the desired product, requiring only basic algebraic manipulation. While it tests understanding beyond rote calculation, it's a standard further maths technique with minimal steps for 3 marks.
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The roots of the equation
$$x^3 - 8x^2 + 28x - 32 = 0$$
are \(\alpha\), \(\beta\) and \(\gamma\).
Without solving the equation, find the value of
$$(\alpha + 2)(\beta + 2)(\gamma + 2).$$
[3 marks]
In this question you must show all stages of your working.
Solutions relying on calculator technology are not acceptable.
The roots of the equation
$$x^3 - 8x^2 + 28x - 32 = 0$$
are $\alpha$, $\beta$ and $\gamma$.
Without solving the equation, find the value of
$$(\alpha + 2)(\beta + 2)(\gamma + 2).$$
[3 marks]
\hfill \mbox{\textit{SPS SPS FM 2021 Q1 [3]}}