Aptitude Questions: Quadratic Equations Set 15

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

1. x² – 18x + 72= 0, 5y² – 18y + 9 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   A) If X>Y
   Explanation:
   x² – 18x + 72= 0
   (x-12)(x-6) = 0
   Gives x = 6, 12
   5y² – 18y + 9 = 0
   5y² – 15y – 3y + 9 = 0
   Gives y = 3/5, 3
   Put on number line
   3/5       3            6               12
   
   
2. x² = 4, 3y² – 4y – 4 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   E) If X=Y or cannot be established
   Explanation:
   x² = 4
   Gives x = 2 , -2
   3y² – 4y – 4 = 0
   3y² – 6y + 2y – 4 = 0
   Gives y = -2/3, 2
   Put on number line
   -2      -2/3        2
   When y = 2, y ≥ x
   When y = -2/3, y > x(-2) and y < x(2)
   So no relation
   
   
3. 6x² – 5x – 6 = 0, 2y² – 13y + 20 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   B) If X < Y
   Explanation:
   6x² – 5x – 6 = 0
   6x² – 9x + 4x – 6 = 0
   Gives x = -2/3, 3/2
   2y² – 13y + 20 = 0
   2y² – 8y – 5y +20 = 0
   Gives y = 4, 5/2
   Put on number line
   -2/3       3/2        5/2        4
   
   
   
4. 2x² – 5x = 0, 2y² + 7y – 4 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   E) If X=Y or cannot be established
   Explanation:
   2x² – 5x = 0
   x(2x-5) = 0
   Gives x = 0, 5/2
   3y² – 7y – 6 = 0
   3y² – 9y + 2y – 6 = 0
   Gives y = -2/3, 3
   Put on number line
   -2/3        0           5/2               3
   
   
   
5. 2x² + 5x + 2= 0, 2y² + 19y + 45 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   A) If X > Y
   Explanation:
   2x² + 5x + 2= 0
   2x² + 4x + x + 2= 0
   Gives x = -1/2, -2
   2y² + 19y + 45 = 0
   2y² + 10y + 9y + 45 = 0
   Gives y= -10/2, -9/2
   Put on number line
   -10/2           -9/2            -2                 -1/2
   
   
6. x² + x – 20 = 0, 2y² + 13y + 15 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   E) If X = Y or relation cannot be established
   Explanation:
   x² + x – 20 = 0
   (x+5)(x-4) = 0
   Gives x = -5, 4
   2y² + 13y + 15 = 0
   2y² + 10y + 3y + 15 = 0
   Gives y = -5, -3/2
   Put on number line
   -5        -3/2              4
   
   
7. 5x² – 7x – 6 = 0, 5y² + 23y + 12 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   C) If X ≥ Y
   Explanation:
   5x² – 7x – 6 = 0
   5x² – 10x + 3x – 6 = 0
   Gives x = -3/5, 2
   5y² + 23y + 12 = 0
   5y² + 20y + 3y + 12 = 0
   Gives y = -4, -3/5
   Put on number line
   -4          -3/5             2
   
   
8. 3x² + 8x + 5 = 0, 2y² + y – 1 = 0
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   D) If X ≤ Y
   Explanation:
   3x² + 8x + 5 = 0
   3x² + 3x + 5x + 5 = 0
   Gives x = -1, -5/3
   2y² + y – 1 = 0
   2y² + 2y – y -1 = 0
   Gives y = -1, 1/2
   put on number line
   -5/3        -1            1/2
   
   
9. 2x + 5y = 23.5, 5x+ 2y = 22
   A) If X > Y
   B) If X < Y
   C) If X ≥ Y
   D) If X ≤ Y
   E) If X = Y or relation cannot be established
   
   Answer & Explanation

   B) If X < Y
   Explanation:
   Solve the equations, x = 3, y = 3.5
   
   
   
10. 2x² – 9x + 10 = 0, 2y² + 7y – 4 = 0
    A) If X > Y
    B) If X < Y
    C) If X ≥ Y
    D) If X ≤ Y
    E) If X = Y or relation cannot be established
    
    Answer & Explanation

    A) If X > Y
    Explanation:
    2x² – 9x + 10 = 0
    2x² – 9x – 5x + 10 = 0
    Gives x = 2, 5/2
    2y² + 7y – 4 = 0
    2y² + 8y – y – 4 = 0
    Gives y = -4, 1/2
    put on number line
    -4        1/2        2       5/2