Equations And Inequations Ques 57
I. $2 x^{2}+7 x+5=0$
II. $3 y^{2}+5 y+2=0$
Directions : In the following questions two equations numbered I and II are given. You have to solve both the equations and give answer
(1) if $x>y$
(2) if $x \geq y$
(3) if $x<y$
(4) if $x \leq y$
(5) if $x=y$ or the relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 57.(4)
Solution: (4) I. $2 x^{2}+7 x+5=0$
$\Rightarrow 2 x^{2}+2 x+5 x+5=0$
$\Rightarrow 2 x(x+1)+5(x+1)=0$
$\Rightarrow(x+1)(2 x+5)=0$
$\Rightarrow x=-1$ or, $\frac{-5}{2}$
II. $3 y^{2}+5 y+2=0$
$\Rightarrow 3 y^{2}+3 y+2 y+2=0$
$\Rightarrow 3 y(y+1)+2(y+1)=0$
$\Rightarrow(y+1)(3 y+2)=0$
$\Rightarrow y=-1$ or, $\frac{-2}{3}$
Clearly, $x \leq y$
BETA
