Equations And Inequations Ques 98
I. $6 x^{2}+5 x+1=0$
II. $2 y^{2}+5 y+3=0$
Directions : In the following questions, two equations numbered I and II are given. You have to solve both the equations and give answer If
(1) $x<y$
(2) $x>y$
(3) $x \leq y$
(4) $x \geq y$
(5) $\quad x=y$ or the relationship cannot be established
Show Answer
Correct Answer: 98.(2)
Solution: (2) I. $6 x^{2}+5 x+1=0$
$\Rightarrow 6 x^{2}+3 x+2 x+1=0$
$\Rightarrow 3 x(2 x+1)+1(2 x+1)=0$
$\Rightarrow(2 x+1)(3 x+1)=0$
$\Rightarrow x=-\frac{1}{2}$ or, $-\frac{1}{3}$
II. $2 y^{2}+5 y+3=0$
$\Rightarrow 2 y^{2}+2 y+3 y+3=0$
$\Rightarrow 2 y(y+1)+3(y+1)=0$
$\Rightarrow(y+1)(2 y+3)=0$
$\Rightarrow y=-1$ or, $-\frac{3}{2}$
Clearly, $x>y$
BETA
