How do you solve #4x ^3 -13x^2 + 11x - 2 = 0#?

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Answer 1 · 2016-03-15T18:40:20

Lets look if there are any roots among the divisors of #-2# which are #+-1# , #+-2#.
We can easily find out that #x=1# and #x=2# are roots.Hence

the original question can be written as follows

#4x^3 -13x^2 + 11x - 2 =(x-1)*(x-2)*(a*x+b)#

By equating the two sides we find out that #a=4# , #b=-1#
hence

#4x^3 -13x^2 + 11x - 2 =(x-1)*(x-2)*(4x-1)#

Finally the roots are

#x_1=1# , #x_2=2# , #x_3=1/4#