Given the equation `2x ^(2) + 8x + 4+ 2z =0,` for what value of z is there exactly one solution for x ?

Answer

2

Explanation

The given equation is `2x ^(2) + 8x +4 + 2z =0,` but there is a common factor of 2 in all the terms, so this becomes `x ^(2) + 4x + 2 +z =0.So a =1,b=4, and c =2 +z.` Set the discriminant `4 ^(2) -4 (1) (2+z)` equal to 0 so that there is only one solution. Expand the equation to `16-8-4z =0.` Thus `8= 4z, and z =2.` Grid in 2.