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.