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

1. (x + 4)² – 8x = 0
2. (x – √2)² – 2(x + 1) = 0

 (v)

The condition (x + 4)2 – 8x = 0 has no genuine roots.

Working on the above condition,

   

   

   

= (0) – 4(1) (16) < 0

Subsequently, the roots are nonexistent.

(vi)

The condition (x – √2)2 – √2(x+1)=0 has two unmistakable and genuine roots.

Improving on the above condition,

   

   

   

   

   

   

Subsequently, the roots are genuine and unmistakable.