Given:
There are 4 equations.
To find:
The complex roots.
Explanation:
A) Considering option A,
[tex]3x^2+2=0[/tex]Let us find the discriminant value.
[tex]\begin{gathered} \Delta=b^2-4ac \\ =0-4(3)(2) \\ =-24<0 \end{gathered}[/tex]Since it is negative. So, it has complex roots.
B) Considering option B,
[tex]\begin{gathered} 3x^2-1=6x \\ 3x^2-6x-1=0 \end{gathered}[/tex]Let us find the discriminant value.
[tex]\begin{gathered} \Delta=b^2-4ac \\ =(-6)^2-4(3)(-1) \\ =48>0 \end{gathered}[/tex]Since it is positive. So, it has real roots.
C) Considering option C,
[tex]\begin{gathered} 2x^2-1=5x \\ 2x^2-5x-1=0 \end{gathered}[/tex]Let us find the discriminant value.
[tex]\begin{gathered} \Delta=b^2-4ac \\ =(-5)^2-4(2)(-1) \\ =33>0 \end{gathered}[/tex]Since it is positive. So, it has real roots.
D) Considering option D,
[tex]\begin{gathered} 2x+1=7x \\ 5x=1 \\ x=\frac{1}{5} \end{gathered}[/tex]So, it has a real solution.
Final answer:
Option A has complex roots.
