Directions for Questions 31 - 35: In each question two equations numbered I and II are given. You have to solve both the equations and mark answer:
I. ${{x}^{2}}-3x-4=0$
II. ${{y}^{2}}-2y+8=0$
$x \lt y$
$x \gt y$
$x\le y$
$x\ge y$
$x=y$ or relationship between $x$ and $y$ cannot be established
Solution
I. ${{x}^{2}}-3x-4=0$
${{x}^{2}}-\left( 4-1 \right)x-4=0$
${{x}^{2}}-4x+x-4=0$
$x\left( x-4 \right)+1\left( x-4 \right)=0$
$\left( x-4 \right)(x+1)=0$
$x=4,~-1$
II. ${{y}^{2}}-2y-8=0$
${{y}^{2}}-\left( 4-2 \right)y-8=0$
${{y}^{2}}-4y+2y-8=0$
$y\left( y-4 \right)+2(y-4)=0$
$\left( y-4 \right)(y+2)=0$
$y=4,~-2$
After comparison of both equations, the conclusion is $x \geq y$.