Let , which means that 





Now substitute:











 is factorable





 =>  or , so you really don't need the

quadratic formula to solve it.  But since the question asked for it, here

it is



a = 1

b = -3

c = 2



 

 

 =>  or 



And no surprise, the roots are still 1 and 2.



 

But remember 





If  then  or  =>  or 



If  then  or 





This gives us a total of four roots for the original quartic (degree 4)

equation as the Fundamental Theorem of Algebra would lead us to suspect.





Just for fun, let's check the notion graphically:











Note that the graph intersects the x-axis in 4 places and the x-coordinates of

these 4 places are equal to the roots or zeros of the given equation.



How very tidy. 

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