Question

determine the natur of the roots

Answer 1

(2x+8)^2
=0

x= -4 and x=-4

Answer 2

first one divide by 4 and get
\[x^2+8x+16=0\] then if you want the "nature of the zeros" compute
\[b^2-4ac=64-64=0\]so there is one solution. meaning it is a perfect square namely
\[(x+4)^2\] and the solution
\[x=-4\]

Answer 3

second one
\[3x^2+12x-3=0\]
\[b^2-4ac=12^2-4\times 3\times -3=144+36=180\] so there are two real solutions

Answer 4

so solve write
\[x^2+4x-1=0\]
\[x^2+4x=1\]
\[(x+2)^2=1+2^2=1+4=5\]
\[x+2=\pm\sqrt{5}\]
\[x=-2\pm\sqrt{5}\]