Quants Questions : Quadratic Equations Set 9

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You have to solve equation I and II ,Give answer
1)If X>Y
2)If X<Y
3)If X≥ Y
4)If X≤ Y           
5)If X=Y or cannot be established

1. I. X²  – 3X + 2= 0
   II. 9Y² – 9Y + 2 = 0
   

   Answer

   Answer – 1)If X>Y
   Explanation :
   (x-1)(x-2) = 0
   X=1,2
   (3y-1)(3y-2) = 0
   Y =1/2,1/3
   1,2,1/2,1/3
   Xxyy => x>y
   
   
   
2. I. X²  – 6X + 8= 0
   II.Y² – 8Y + 15 = 0
   

   Answer

   Answer – 5)If X=Y or cannot be established
   Explanation :
   (x-4)(x-2) = 0
   X=4,2
   (y-5)(y-3) = 0
   Y=5,3
   5,4,3,2 = yxyx
   
   
   
3. I. 2X²  – 3X – 2= 0
   II. 6Y² + 7Y + 2 = 0
   

   Answer

   Answer – 3)If X≥ Y
   Explanation :
   (x-2)(2x+1) = 0
   X=2,-1/2
   (3x+2)(2x+1) = 0
   X=-2/3,-1/2
   2,-0.5,-0.5, -0.6
   Xxyy => X≥ Y
   
   
   
4. I. 2X²  + 7X + 6= 0
   II. 2Y² + Y – 3 = 0
   

   Answer

   Answer – 4)If X≤ Y
   Explanation :
   (x+2)(2x+3) = 0
   X= -2,-3/2
   (2y+3)(y-1) = 0
   Y=1,-3/2
   1,-3/2,-3/2,-2
   yyxx => X≤ Y
   
   
   
5. I. 6X²  + 11X + 3= 0
   II. 3Y² – 2Y – 1 = 0
   

   Answer

   Answer – 4)If X≤ Y
   Explanation :
   (3x+1)(2x+3) = 0
   X= -1/3, -3/2
   (y-1)(3y+1) = 0
   Y = 1,-1/3
   1,-1/3,-1/3,-3/2
   Yyxx => X≤ Y
   
   
   
6. I. 5X²  – 126X + 25= 0
   II. 9Y² – 22Y + 8 = 0
   

   Answer

   Answer – 5)If X=Y or cannot be established
   Explanation :
   (5x-1)(x-25) = 0
   X=1/5, 25
   (y-2)(9y-4) = 0
   Y = 2,4/9
   25,2,4/9,1/5
   Xyyx
   
   
   
7. I. 2X²  – 9X + 7= 0
   II. 6Y² + 7Y – 10 = 0
   

   Answer

   Answer – 1)If X>Y
   Explanation :
   (2x-7)(x-1) = 0
   X=7/2,1
   (y+2)(6y-5) = 0
   y= -2, 5/6
   7/2,1,5/6, -2
   Xxyy = x>y
   
   
   
8. I. X  + 1/x  = 10/3
   II. 4-11y = 3y²
   

   Answer

   Answer – 3)If X≥ Y
   Explanation :
   (3x-1)(x-3) = 0
   X=3,1/3
   (3y-1)(y+4) = 0
   Y = 1/3,-4
   3,1/3,1/3, -4
   Xxyy = > X≥ Y
   
   
   
9. I. X= (1024)^1/2
   II. Y² = 1024
   

   Answer

   Answer – 3)If X≥ Y
   Explanation :
   X = 32
   Y=±32
   x≥y
   
   
   
10. I. X²  – 20X = -91
    II. 3Y² = 22Y – 32
    

    Answer

    Answer – 1)If X>Y
    Explanation :
    (x-7)(x-13) = 0
    X=7,13
    (3x-16)(x-2) = 0
    X=2,16/3
    7,13,16/3,2
    Xxyy = x>y