Question 129562
{{{ graph( 500, 500, -30, 30, -30, 30, x^5 - x^3 -8x^2 + 8) }}} 


by observing the graph we cn find that -1 and +1 are the first twoo roots. 

The other 3 roots are repeated roots and it would be 2.


This can be factorised by the method of trail and error method and then by synthetic division method.


by the trail and error method we find that 1 is the first factor


{{{(x - 1)(x^4 + x^3 - 8x - 8)}}} 


Then the second equation is agin siplified


here we find that x + 1 is a factor.


So {{{(x - 1)(x + 1)(x^3 - 8) }}} will be the next eqn.



So the last eqn will be {{{(x^3 - 8)}}} can be factored and thus we get repeated roots 


hence, the roots are x = 1, -1, 2, 2, 2


(x - 1)(x + 1)(x- 2)(x - 2)(x - 2)


Are the roots of the eqn


Thus the solution


Regards
Chitra