[tex]y = 2 {x}^{3} - 7 {x}^{2} + 2x + 3[/tex]
By inspection 1 is a root of y ,
Hence , (x-1) is a factor of y ,
[tex] \dfrac{2 {x}^{3} - 7 {x}^{2} + 2x + 3 }{x - 1} = 2 {x}^{2} - 5x - 3 \\ \\ 2 {x}^{2} - 5x - 3 = (2x + 1)(x - 3)[/tex]
Hence , the 2 other roots are -1/2 and 3 , and the above graphs confirms the same.
Hope it helps you :)
