Equations And Inequations Ques 64
I. $15 x^{2}+26 x+8=0$
II. $25 y^{2}+15 y+2=0$
Directions : In each of these questions, two equations (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 relationship between $x$ and $y$ cannot be established.
Show Answer
Correct Answer: 64.(4)
Solution: (4) I. $15 x^{2}+26 x+8=0$
$\Rightarrow 15 x^{2}+20 x+6 x+8=0$
$\Rightarrow 5 x(3 x+4)+2(3 x+4)=0$
$\Rightarrow(3 x+4)(5 x+2)=0$
$\Rightarrow x=-\frac{4}{3}$ or $-\frac{2}{5}$
II. $25 y^{2}+15 y+2=0$
$\Rightarrow 25 y^{2}+10 y+5 y+2=0$
$\Rightarrow 5 y(5 y+2)+1(5 y+2)=0$
$\Rightarrow(5 y+2)(5 y+1)=0$
$\Rightarrow y=-\frac{2}{5}$ or, $-\frac{1}{5}$
Clearly, $x \leq y$
BETA
