Question

In the following question, two equations numbered I and II are given. Solve both the equations and mark the appropriate option:
I. $x^2-11x+24=0$
II. $2y^2-9y+9=0$

• A. if x > y
• B. if x y
• C. if x < y
• D. if xy
• E. if x = y or the relationship cannot be established

Answer 1

The correct option is B

if x y

I. $x^2-11x+24=0$
$\Rightarrow$ $x^2-8x-3x+24=0$
$\Rightarrow$ $x(x-8)-3(x-8)=0$
$\Rightarrow$ $(x-3)(x-8)=0$
$\therefore x=3or8$
II. $2y^2-9y+9=0$
$\Rightarrow$ $2y^2-3y-6y+9=0$
$\Rightarrow$ $y(2y-3)-3(2y-3)=0$
$\Rightarrow$ $2y-3\left)\right(y-3)=0$
$\therefore$ $y=\frac{3}{2}or3$
Clearly, $x\ge y$