question_answer

Directions : In these questions, two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer.                                                                [NICL (AO) 2014]

I. \[22{{x}^{2}}-x-6=0\]

II. \[63{{y}^{2}}-11y-40=0\]

A) If \[x\le y\]

B) lf \[x<y\]

C) If \[x>y\]

D) If relationship between x and y cannot be established

E) lf \[x\ge y\]

Correct Answer: D

Solution :

I. \[22{{x}^{2}}-x-6=0\]

By splitting the middle term,

\[22{{x}^{2}}+11x-12x-6=0\]

\[11x\,(2x+1)-6\,(2x+1)=0\]

\[(11x-6)(2x+1)=0\]

\[x=\frac{6}{11},\]\[x=-\frac{1}{2}\]

value of \[x=\left( \frac{6}{11},\,-\frac{1}{2} \right)\]

II. \[63{{y}^{2}}-11y-40=0\]

By splitting the middle term.

\[63{{y}^{2}}+45y-56y-40=0\]

\[9y\,(7y+5)-8\,(7y+5)=0\]

\[(9y-8)(7y+5)=0\]

\[y=\frac{8}{9},\]\[y=-\frac{5}{7}\]

value of \[y=\left( \frac{8}{9},-\frac{5}{7} \right)\]

Hence, relationship between x and y cannot be established.