Easy -1.2 This is a direct recall question requiring only knowledge of Vieta's formulas for a cubic polynomial. Students simply need to identify that αβ + βγ + γα = c/a = -3/5 with no calculation or problem-solving required. The multiple-choice format and single-step nature make this significantly easier than average A-level questions.
4 The roots of the equation
$$5 x ^ { 3 } + 2 x ^ { 2 } - 3 x + p = 0$$
are \(\alpha , \beta\) and \(\gamma\)
Given that \(p\) is a constant, state the value of \(\alpha \beta + \beta \gamma + \gamma \alpha\)
Circle your answer.
\(- \frac { 3 } { 5 }\)
\(- \frac { 2 } { 5 }\)
\(\frac { 2 } { 5 }\)
\(\frac { 3 } { 5 }\)
4 The roots of the equation
$$5 x ^ { 3 } + 2 x ^ { 2 } - 3 x + p = 0$$
are $\alpha , \beta$ and $\gamma$
Given that $p$ is a constant, state the value of $\alpha \beta + \beta \gamma + \gamma \alpha$
Circle your answer.\\
$- \frac { 3 } { 5 }$\\
$- \frac { 2 } { 5 }$\\
$\frac { 2 } { 5 }$\\
$\frac { 3 } { 5 }$
\hfill \mbox{\textit{AQA Further AS Paper 1 2023 Q4 [1]}}