Easy -1.2 This is a direct application of Vieta's formulas requiring only recall of the standard result that for ax³+bx²+cx+d=0, the sum of products of roots taken two at a time equals c/a. Here, αβ+βγ+γα = -4/20 = -1/5. It's a 1-mark multiple-choice question testing basic knowledge with no problem-solving or manipulation required, making it easier than average even for Further Maths.
The roots of the equation \(20x^3 - 16x^2 - 4x + 7 = 0\) are \(\alpha\), \(\beta\) and \(\gamma\)
Find the value of \(\alpha\beta + \beta\gamma + \gamma\alpha\)
Circle your answer.
[1 mark]
\(-\frac{4}{5}\) \(-\frac{1}{5}\) \(\frac{1}{5}\) \(\frac{4}{5}\)
The roots of the equation $20x^3 - 16x^2 - 4x + 7 = 0$ are $\alpha$, $\beta$ and $\gamma$
Find the value of $\alpha\beta + \beta\gamma + \gamma\alpha$
Circle your answer.
[1 mark]
$-\frac{4}{5}$ $-\frac{1}{5}$ $\frac{1}{5}$ $\frac{4}{5}$
\hfill \mbox{\textit{AQA Further Paper 1 2024 Q1 [1]}}