Question 43
(ROM 2) The equation
$$x^5+5\lambda x^4-x^3+(\lambda\alpha-4)x^2-(8\lambda+3)x+\lambda\alpha-2=0$$
is given.
(a) Determine $\alpha$ such that the given equation has exactly one root independent of $\lambda$.
(b) Determine $\alpha$ such that the given equation has exactly two roots independent of $\lambda$.
$$x^5+5\lambda x^4-x^3+(\lambda\alpha-4)x^2-(8\lambda+3)x+\lambda\alpha-2=0$$
is given.
(a) Determine $\alpha$ such that the given equation has exactly one root independent of $\lambda$.
(b) Determine $\alpha$ such that the given equation has exactly two roots independent of $\lambda$.