Question

In a three dimensional space the equation $ {{x}^{2}}-5x+6=0 $ represents

• A. points
• B. planes
• C. curves
• D. None of these

Answer 1

Answer: (B)

Given equation is $ {{x}^{2}}-5x+6=0 $ ..(i)
we know that the standard equation of plane in three dimensional space is $ ax+by+cz+d=0 $
Now, from Eq. (i) $ {{x}^{2}}-3x-2x+6=0 $
$ \Rightarrow $ $ x(x-3)-2(x-3)=0 $
$ \Rightarrow $ $ (x-3)(x-2)=0 $
$ \therefore $ $ x-3=0 $ and $ x-2=0 $
$ \Rightarrow $ $ 1.x+0.y+0.z-3=0 $
and $ 1.x+0.y+0.z-2=0 $
So, both represents equations of plane.