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Aptitude Questions: Quadratic Equations Set 12

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Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions in Quadratic Equations which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

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

    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

    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

    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

    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

    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

    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

    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

    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

    B) If X < Y
    Explanation:

    Solve the equations, x = 3, y = 3.5

  10. 2x2 – 9x + 4 = 0,
    2y2 + 7y – 4 = 0

    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