Quantitative Aptitude: Quadratic Equations Set 14

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-

  1. I. 3x2 + 22x + 24 = 0,
    II. 3y2 – 8y – 16 = 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
    View Answer
    Option D
    Solution:

    3x2 + 22 x + 24 = 0
    3x2 + 18x + 4x + 24 = 0
    Gives x = -4/3, -6
    3y2 – 8y – 16 = 0
    3y2 – 12y + 4y – 16 = 0
    So y = -4/3, 4
    Plot on number line
    -6…. -4/3……. 4
  2. I. 5x2 – 18x – 8 = 0,
    II. 2y2 + 11y + 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
    View Answer
    Option A
    Solution:

    5x2 – 18x – 8 = 0
    5x2 – 20x + 2x – 8 = 0
    So x = -2/5, 4
    2y2 + 11y + 12 = 0
    2y2 + 8y + 3y + 12 = 0
    Gives y = -4, -3/2
    Plot on number line
    -4… -3/2…. -2/5….. 4
  3. I. x2 – 652 = 504,
    II. y = √1156
    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
    View Answer
    Option D
    Solution:

    x2 – 652 = 504
    x2 = 1156
    So x = 34, -34
    y = √1156 = 34
    Plot on number line
    -34… 34
  4. I. 9/√x + 8/(√x +1) = 5,
    II. 12/√y – 4/√y = 2
    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
    View Answer
    Option B
    Solution:

    9/√x + 8/(√x +1) = 5
    [9(√x +1) + 8√x]/[√x * (√x +1)] = 5
    17√x + 9 = 5 (x + √x)
    5x – 12√x – 9 = 0
    5x – 15√x + 3√x – 9 = 0
    5√x (√x – 3) + 3 (√x – 3) = 0
    √x cannot be -3/3
    So √x = 3, so x = 9
    12/√y – 4/√y = 2
    8/√y = 2
    So √y = 4 or y = 16
    So y > x
  5. I. 3x2 – 6x – √3x + 2√3 = 0,
    II. 2y2 – 3y – 2√2y + 3√2 = 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
    View Answer
    Option E
    Solution:

    3x2 – 6x – √3x + 2√3 = 0
    3x (x- 2) – √3 (x – 2) = 0,
    So x = 2, √3/3
    2y2 – 3y – 2√2y + 3√2 = 0
    y (2y – 3) – √2 (2y – 3) = 0
    So y = 3/2, √2 (1.44)
    plot on number line
    √3/3(0.57)…….√2…..(3/2)……2
  6. I. x2 – 2x – √5x + 2√5 = 0
    II. y2 – 3y – √6y + 3√6 = 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
    View Answer
    Option B
    Solution:

    x2 – 2x – √5x + 2√5 = 0
    x (x – 2) – √5 (x – 2) = 0
    So x = 2, √5 (2.23)
    y2 – 3y – √6y + 3√6 = 0
    y (y – 3) – √6 (y – 3) = 0
    So y = 3, √6 (2.44)
    Plot on number line
    2…2.23……2.44…….3
  7. I. 8x2 + 6x + 1 = 0,
    II. 5y2 + 8y – 4 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option E
    Solution:

    8x2 + 6x + 1 = 0
    8x2 + 4x + 2x + 1 = 0
    So x = -1/4, -1/2
    5y2 + 8y – 4 = 0
    5y2 + 10y – 2y – 4 = 0
    So y = -2, 2/5
  8. I. 4x2 – 23x + 30 = 0,
    II. 4y2 – 3y – 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
    View Answer
    Option E
    Solution:

    4x2 – 23x + 30 = 0
    4x2 – 15x – 8x + 30 = 0
    So x = 15/4, 2
    4y2 – 3y – 45 = 0
    4y2 + 12y – 15y – 45 = 0
    So y = -3, 15/4
    Put on number line
    -3…. 2…. 15/4
  9. I. 5x2 – 7x – 6 = 0,
    II. 3y2 – 2y – 8 = 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
    View Answer
    Option E
    Solution:

    5x2 – 7x – 6 = 0
    5x2 – 10x + 3x – 6 = 0
    So x = -3/5, 2
    3y2 – 2y – 8 = 0
    3y2 – 6y + 4y – 8 = 0
    So y = -4/3, 1
    Plot on number line
    -4/3……-3/5….. 1….. 2
  10. I. 3x2 + 2x – 21 = 0,
    II. 3y2 – 19y + 28 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
    Option D
    Solution:

    3x2 + 2x – 21 = 0
    3x2 + 9x – 7x – 21 = 0
    Gives x = -3, 7/3
    3y2 – 19y + 28 = 0
    3y2 – 12y – 7y + 28 = 0
    So y = 7/3, 4
    Put on number line
    -3……7/3……4

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