Question

Find the complex root of 8x^2+16x+8

Answer 1

S={-1}

1) Let's solve this equation.

8x² +16x +8

2) Notice that the discriminant yields 0

`\begin{gathered} \Delta=b^2-4ac \\ \Delta=16^2-4(8)(8)=-240 \\ x=\frac{-b\pm\sqrt[]{\Delta}}{2a}=\frac{-16\pm\sqrt[]{0}}{2(8)} \\ x_1=x_2=(-16)/(16)=-1 \end{gathered}`

3) Since every real number is complex too as the Real set as a subset of the Complex Numbers set, hence, we can state that the root is also complex and it is -1

S={-1}

As the Discriminant is zero then, the parabola touches the x-axis on one single point x =-1.