?. x ² ? 11x + 24 = 0
?. 2y ² ? 9y + 9 = 0

Given :- x² - x - 2 = 0
The given equation is of the form
ax² + bx + c = 0
Here , a = 1 , b = -1 , c = - 2
Now, D² = b² - 4ac = ( -1 )² - 4 x 1 x ( - 2 )
D = ?9 = 3
So, roots are rational .
Hence, both the roots must be integers.

Given :- Px² + 4x + 1 = 0
Compare with Ax ² + Bx + C = 0, we get
A = P, B = 4, C = 1
For real roots,
B² - 4AC ? 0
? 16 - 4P ? 0
? 16 ? 4P
? P ? 16/4 ? P ? 4.
Hence , required answer is option C .

As per the given above equations , we can say that
?.
?500x + ?402 = 0
? ?500x = - ?402
? x = - ?( 402/500 ) = - ?( 400/500 ) = - 0.9
?. ?360y + ( 200 )^1/2 = 0
? ?360y = - ?200
?
y = - ?( 200 / 360 ) = - 0.74
Clearly, we can see that x < y is required answer .

As per the given above question , we have
Let, x = 6 + ?6 + ?6 + ?6 +........
On squaring both sides, we have
x² = 6 + ?6 + ?6 + ?6 +........
? x² = 6 + x
? x² - x - 6 = 0
? x² - 3x + 2x - 6 = 0
? x( x - 3 ) + 2( x - 3 ) = 0
? ( x - 3 ) ( x + 2 ) = 0
? x = 3 and x ? ?2 because numbers are positive.
Thus , correct answer will be 3 .