State whether the following quadratic equations have two distinct real roots. Justicy your answer:
`(x+4)^(2)-8x=0`

Explanation

Given equation is `(x+4)^(2)-8x=0`
`implies x^(2)+16-8x-8x=0 [ :' (a+b)^(2)=a^(2)+2ab+b^(2)]`
`implies x^(2)+16=0`
`implies x^(2)+0.x+16=0`
On comparing with `ax^(2)+bx+c=0` we get
`a=1, b=0` and `c=16`
`:.` Discriminant `D=b^(2)-4ac=(0)^(2)-4(1)(16)=-64lt0` i.e. `Dlt0`
Hence the equation `(x+4)^(2)-8x=10` has imaginary roots, i.e. no real roots.