Equations And Inequations Ques 121
I. $2 x^{2}+17 x+30=0$
II. $6 y^{2}-5 y-6=0$
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: 121.(3)
Solution: (3) $2 x^{2}+17 x+30=0$
$\Rightarrow 2 x^{2}+5 x+12 x+30=0$
$\Rightarrow x(2 x+5)+6(2 x+5)=0$ $\Rightarrow(x+6)(2 x+5)=0$
$\Rightarrow x=-6$ or, $-\frac{5}{2}$
$=-6$ or, -2.5
II. $6 y^{2}-5 y-6=0$
$\Rightarrow 6 y^{2}-9 y+4 y-6=0$
$\Rightarrow 3 y(2 y-3)+2(2 y-3)=0$
$\Rightarrow(2 y-3)(3 y+2)=0$
$\Rightarrow y=\frac{3}{2}$ or, $-\frac{2}{3}$
$=1.5$ or, -0.67
Clerly, $x<y$
BETA
