State whether the following quadratic equations have two distinct real roots. Justify your answer.

(x + 1) (x - 2) + x = 0


The equation (x + 1) (x - 2) + x = 0 has two real and distinct roots.


Simplifying the above equation,


x2 + x – 2x – 2 + x = 0


x2 – 2 = 0


D = b2 - 4ac


= (0)2 - 4(1) (-2)


= 0 + 8 > 0


Hence, the roots are real and distinct.


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