Aptitude Questions: Quadratic Equations Set 12

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Follow the link To solve Quadratic Equations with the help of Number Line

You have to solve equation I and II ,Give answer
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or cannot be established

1. x² – 18x + 72= 0,
   3y² + 7y + 4 = 0
   
   Answer & Explanation

   A) If X > Y
   Explanation:
   x² – 18x + 72= 0
   (x-12)(x-6) = 0
   x = 6, 12
   3y² + 7y + 4 = 0
   (y+1)(3y+4) = 0
   y = -1, -4/3
   Put on number line
   -4/3        -1               6               12
   
   
   
2. x² = 4,
   y² + y – 6 = 0
   
   Answer & Explanation

   E) If X = Y or cannot be established
   Explanation:
   x² = 4
   x = 2 , -2
   y² + y – 6 = 0
   (y+3)(y-2) = 0
   y = -3, 2
   put on number line
   -3                     -2                   2
   When y = -3, y < x
   When y = 2, y ≥ x
   So no relation
   
   
3. 2x² + x – 36 = 0,
   2y² – 13y + 20 = 0
   
   Answer & Explanation

   E) If X = Y or cannot be established
   Explanation:
   2x² + x – 36 = 0
   2x² – 8x + 9x – 36 = 0
   x = 4 , -9/2
   2y² – 13y + 20 = 0
   2y² – 8y – 5y +20 = 0
   2y(y-4) – 5(y-4) = 0
   y = 4, 5/2
   put on number line
   -9/2                     5/2                         4
   
   
   
4. x² – 5x = 0,
   2y² + 7y – 4 = 0
   
   Answer & Explanation

   E) If X = Y or cannot be established
   Explanation:
   x² – 5x = 0
   x(x-5) = 0
   x = 0, 5
   2y² + 7y – 4 = 0
   2y² + 8y – y – 4 = 0
   y = -4, 1/2
   put on number line
   -4               0                    1/2                    5
   
   
   
5. 2x² + 5x + 2= 0,
   2y² + 19y + 45 = 0
   
   Answer & Explanation

   A) If X > Y
   Explanation:
   2x² + 5x + 2= 0
   (2x+1)(x+2) =0
   X= -1/2, -2
   2y² + 19y + 45 = 0
   (2y+10)(2y+9) = 0
   Y= -10/2, -9/2 = -5, -4.5
   Put on number line
   -5                  -4.5                      -2                        -1/2
   
   
6. x² + x – 20 = 0,
   y² – 13y + 40 = 0
   
   Answer & Explanation

   B) If X < Y
   Explanation:
   x² + x – 20 = 0
   (x+5)(x-4) = 0
   x = -5, 4
   y² – 13y + 40 = 0
   (y-5)(y-8) = 0
   y = 5, 8
   
   
7. x² – 11x + 24 = 0,
   y² + 9y + 18 = 0
   
   Answer & Explanation

   A) If X > Y
   Explanation:
   x² – 11x + 24 = 0
   (x-3)(x-8) = 0
   x = 3, 8
   y² + 9y + 18 = 0
   (y+3)(y+6) = 0
   y = -3, -6
   put on number line
   -6                -3                  3                      8
   
   
8. 3x² + 8x + 5 = 0,
   2y² + y – 1 = 0
   
   Answer & Explanation

   D) If X ≤ Y
   Explanation:
   3x² + 8x + 5 = 0
   3x² + 3x + 5x + 5 = 0
   x = -1, -5/3
   2y² + y – 1 = 0
   2y² + 2y – y -1 = 0
   y = -1, 1/2
   put on number line
   -5/3                     -1                   1/2
   
   
9. 3x + 2y = 16,
   2x+ 3y = 33/2
   
   Answer & Explanation

   B) If X < Y
   Explanation:
   Solve the equations, x = 3, y = 3.5
   
   
   
10. 2x² – 9x + 4 = 0,
    2y² + 7y – 4 = 0
    
    Answer & Explanation

    C) If X ≥ Y
    Explanation:
    2x² – 9x + 4 = 0
    2x² – 8x – x + 4 = 0
    x = 4 , 1/2
    2y² + 7y – 4 = 0
    2y² + 8y – y – 4 = 0
    y = -4, 1/2
    put on number line
    -4                 1/2                         4