Question 541523
Find all solutions: (You should expect to get 6 solutions, some of which might be identical)
{{{4t^6-t^4 = 0}}} Factor out {{{t^4}}}
{{{t^4(t^2-1) = 0}}} Apply the "zero product rule".
{{{t^4 = 0}}} or {{{t^2-1 = 0}}}
If {{{t^4 = 0}}} then {{{t*t*t*t = 0}}} and {{{t = 0}}} is a solution four times.
{{{4t^2-1 = 0}}} Factor this.
{{{(2t+1)(2t-1) = 0}}} Apply the "zero product rule"'
{{{2t+1 = 0}}} or {{{2t-1 = 0}}} so...
{{{2t = -1}}} and {{{t = -1/2}}}
{{{2t = 1}}} and {{{t = 1/2}}}
The six solutions (four of which are identical) are:
{{{t = 0}}}
{{{t = 0}}}
{{{t = 0}}}
{{{t = 0}}}
{{{t = -1/2}}}
{{{t = 1/2}}}
To give some idea of the graphical soltions:
{{{graph(400,400,-3,3,-5,5,4x^6-x^4)}}}