Equations And Inequations Ques 123
I. $2 x^{2}+5 x+2=0$
II. $4 y^{2}-7 y-2=0$
Directions : In each of these questions, two equations I and II are given. Solve both the equations and select the appropriate answer from the codes given below.
(1) If $x>y$
(2) If $x \geq y$
(3) If $x<y$
(4) If $x \leq y$
(5) If $x=y$ or no relationship can be established between $x$ and $y$
Show Answer
Correct Answer: 123.(3)
Solution: (3) I. $2 x^{2}+5 x+2=0$
$\Rightarrow 2 x^{2}+4 x+x+2=0$
$\Rightarrow 2 x(x+2)+1(x+2)=0$
$\Rightarrow(x+2)(2 x+1)=0$
$\Rightarrow x=-2$ or, $-\frac{1}{2}$
$=-2$ or, -0.5
II. $4 y^{2}-7 y-2=0$
$\Rightarrow 4 y^{2}-8 y+y-2=0$
$\Rightarrow 4 y(y-2)+1(y-2)=0$
$\Rightarrow(4 y+1)(y-2)=0$
$\Rightarrow y=2$ or $-\frac{1}{4}$
$\Rightarrow 2$ or, -0.25
Clearly, $x<y$
BETA
