Directions (51 - 55): In these questions two equations numbered I and II are given. You have to solve both the equations and give answer.
Give Answer (A) if $x \lt y$
Give Answer (B) if $x \gt y$
Give Answer (C) if $x \le y$
Give Answer (D) if $x \ge y$
Give Answer (E) if $x = y$ or relationship between $x$ & $y$ can not be established
I. $7{{x}^{2}}+20x+12=0$
II. $21{{y}^{2}}+2y-3=0$
$x \lt y$
$x \gt y$
$x \le y$
$x \ge y$
$x = y$ or relationship between $x$ & $y$ can not be established
Solution
I.
$\begin{align}
& 7{{x}^{2}}+20x+12=0 \\
& \Rightarrow 7{{x}^{2}}+14x+6x+12=0 \\
& \Rightarrow 7x(x+2)+6(x+2)=0 \\
& \Rightarrow (7x+6)(x+2)=0 \\
& \Rightarrow x=-\frac{6}{7}or-2 \\
\end{align}$
II.
$\begin{align}
& 21{{y}^{2}}+2y-3=0 \\
& \Rightarrow 21{{y}^{2}}-7y+9y-3=0 \\
& \Rightarrow 7y(3y-1)+3(3y-1)=0 \\
& \Rightarrow (7y+3)(3y-1)=0 \\
& \Rightarrow y=-\frac{3}{7}or-\frac{1}{3} \\
\end{align}$
So, $x \lt y$