The roots $\alpha,\ \beta,\ \gamma,\ \delta$ of a quartic equation satisfy $\sum\alpha=2$, \(\su

Question

The roots $\alpha,\ \beta,\ \gamma,\ \delta$ of a quartic equation satisfy $\sum\alpha=2$, $\sum\alpha\beta=-7$, $\sum\alpha\beta\gamma=-8$ and $\alpha\beta\gamma\delta=12$. Write down this quartic equation in the form $x^4+bx^3+cx^2+dx+e=0$. Verify that $-2$ is a root of the equation found in **(a)**.

Accepted Answer

(a) $x^4-2x^3-7x^2+8x+12=0$ (b) shown

Constructing a quartic from symmetric data

Constructing a quartic from symmetric data

Solution:

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