Equations And Inequations Ques 175
I. $2 x^{2}+15 x+28=0$
II. $4 y^{2}+18 y+14=0$
Directions : In the following questions, two equations I and II have been given. You have to solve both equations and give answer if
(1) $x>y$
(2) $x \geq y$
(3) $x<y$
(4) $x \leq y$
(5) $x=y$ or the relation cannot be established.
(IBPS RRBs Officer Scale-I CWE, 06.09.2014)
Show Answer
Correct Answer: (4)
Solution: (4) I. $2 x^{2}+15 x+28=0$
$\Rightarrow 2 x^{2}+8 x+7 x+28=0$
$\Rightarrow 2 x(x+4)+7(x+4)=0$
$\Rightarrow(2 x+7)(x+4)=0$
$\Rightarrow x=-\frac{7}{2}$ or -4
II. $4 y^{2}+18 y+14=0$
$\Rightarrow 2 y^{2}+9 y+7=0$
$\Rightarrow 2 y^{2}+2 y+7 y+7=0$
$\Rightarrow 2 y(y+1)+7(y+1)=0$
$\Rightarrow(2 y+7)(y+1)=0$
$\Rightarrow y=-\frac{7}{2}$ or -1
Clearly, $x \leq y$
BETA
