CAIE A-Level Further Math AS 1.1.1 Polynomial Roots Questions

$\alpha^{2} \beta^{2} \gamma^{2} \delta^{2}=25$

B1FT

$\frac{1}{\alpha^{2}}+\frac{1}{\beta^{2}}+\frac{1}{\gamma^{2}}+\frac{1}{\delta^{2}}=\frac{\alpha^{2} \beta^{2} \delta^{2}+\alpha^{2} \beta^{2} \gamma^{2}+\beta^{2} \gamma^{2} \delta^{2}+\alpha^{2} \gamma^{2} \delta^{2}}{\alpha^{2} \beta^{2} \gamma^{2} \delta^{2}}$
Relates to coefficients.

$\frac{14}{25}$
CAO

3

$$\begin{aligned} \alpha^{4}+\beta^{4}+\gamma^{4}+\delta^{4}= \left(\alpha^{2}+\beta^{2}+\gamma^{2}+\delta^{2}\right)^{2} \quad-2\left(\alpha^{2} \beta^{2}+\alpha^{2} \gamma^{2}+\alpha^{2} \delta^{2}+\beta^{2} \gamma^{2}+\beta^{2} \delta^{2}+\gamma^{2} \delta^{2}\right) = 2^{2}-2(11) \end{aligned}$$
Uses formula for sum of squares or uses original equation.

-18
2