Equations And Inequations Ques 166
I. $6 x^{2}+41 x+63=0$
II. $12 y^{2}+55 y+63=0$
Directions : In each of the following questions two equations I and II have been 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 relationship cannot be established between them
(IDBI Officer Grade Exam. 22.08.2014)
Show Answer
Correct Answer: (4)
Solution: (4) I. $6 x^{2}+41 x+63=0$
$\Rightarrow 6 x^{2}+27 x+14 x+63=0$
$\Rightarrow 3 x(2 x+9)+7(2 x+9)=0$
$\Rightarrow(3 x+7)(2 x+9)=0$
$\therefore x=\frac{-7}{3}$ or $\frac{-9}{2}$ II. $12 y^{2}+55 y+63=0$
$\Rightarrow 12 y^{2}+27 y+28 y+63=0$
$\Rightarrow 3 y(4 y+9)+7(4 y+9)=0$
$\Rightarrow(3 y+7)(4 y+9)=0$
$\Rightarrow y=\frac{-7}{3}$ or $\frac{-9}{4}$
Clearly, $x \leq y$
BETA
