Equations And Inequations Ques 92
I. $3 x^{2}+13 x+12=0$
II. $4 y^{2}+5 y+1=0$
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: 92.(1)
Solution: (1) I. $3 x^{2}+13 x+12=0$
$\Rightarrow 3 x^{2}+9 x+4 x+12=0$
$\Rightarrow 3 x(x+3)+4(x+3)=0$
$\Rightarrow(x+3)(3 x+4)=0$
$\Rightarrow x=-3$ or, $-\frac{4}{3}$
II. $4 y^{2}+5 y+1=0$
$\Rightarrow 4 y^{2}+4 y+y+1=0$
$\Rightarrow 4 y(y+1)+1(y+1)=0$
$\Rightarrow(y+1)(4 y+1)=0$
$\Rightarrow y=-1$ or, $-\frac{1}{4}$
Clearly $x<y$
BETA
