When -5<=a<=5, the equation x^5-(a^2+4)x^3+x^2+a^2 x+2a+1=0 has 3, 4 or 5 solutions, depending on the value of a. Use a dynamic plot of the graph of the left side of this equation to determine the values of a for which the equation has: 3, 4, and 5 solutions. Can anyone help show me how to find these solutions?
Did you mean something like this?
Manipulate[ Plot[x^5 - (a^2 + 4) x^3 + x^2 + a^2 x + 2 a + 1, {x, -3, 3}, PlotRange -> {-40, 40}], {{a, 0}, -5, 5}]
