The equation $2x^4+px^3+qx^2+3x-6=0$ has roots $\alpha,\ \beta,\ \gamma,\ \delta$. The sum of th

Question

The equation $2x^4+px^3+qx^2+3x-6=0$ has roots $\alpha,\ \beta,\ \gamma,\ \delta$. The sum of the roots is $\dfrac{5}{2}$ and the sum of the products of pairs of roots is $-\dfrac{3}{2}$. Find the values of $p$ and $q$. Write down the values of $\sum\alpha\beta\gamma$ and $\alpha\beta\gamma\delta$.

Accepted Answer

(a) $p=-5,\ q=-3$ (b) $\sum\alpha\beta\gamma=-\frac{3}{2},\ \alpha\beta\gamma\delta=-3$

Unknown coefficients in a quartic

Unknown coefficients in a quartic

Solution:

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