Question

The $x$-coordinate of the vertices of a square of unit area are the roots of the equation $x^2-3|x|+2=0$ and the $y$-coordinates of the vertices are the roots of the equation $y^2-5y+6=0$. The number of such square is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B

2

$x^2$ - 3 |x| + 2 = 0 $\Rightarrow$ |$x^2$| - 3 |x| + 2 = 0
$\Rightarrow$ x = $\pm$ 1, $\pm$ 2
and $y^2$ - 5y + 6 = 0 $\Rightarrow$ y = 2, 3

So the vertices can be (-1, 2), (-1, 3), (-2, 3), (-2, 2) or (1,2), (2, 3), (2,2), (1,3)
Both are of unit area
Hence there are 2 such squares.