Quantitative Aptitude: Quadratic Equations Set 8 (New Pattern)

  1. I. 2x2 – 15√3x + 84 = 0
    II. 3y2 – 10√3y + 9 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option A
    Solution:

    2x2 – 15√3x + 84 = 0
    Now multiply 2 and 84 = 168
    we have √3 in equation, so divide, 168/3 = 56
    Now make factors so as by multiply you get 56, and by addition or subtraction you get –15
    we have factors (-8) and (-7)
    So 2x2 – 15√3x + 84 = 0
    gives
    2x2 – 8√3x – 7√3x + 84 = 0
    2x (x – 4√3) – 7√3 (x – 4√3x) = 0
    So x = 7√3/2, 4√3
    Similarly for
    3y2 – 10√3y + 9 = 0
    Multiply 3 and 9 = 27
    we have √3 in equation, so divide, 27/3 = 9
    Now make factors so as by multiply you get 9, and by addition or subtraction you get –10
    we have factors (-9) and (-1)
    So 3y2 – 10√3y + 9 = 0
    gives
    3y2 – 9√3y – √3y + 9 = 0
    3x (x – 3√3) – √3 (x – 3√3x) = 0
    Put all values on number line and analyze the relationship
    √3/3 …. 3√3 ….. 7√3/2 …… 4√3
  2. I. x2 + √5x – 10 = 0
    II. 2y2 + 9√5y + 50 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option C
    Solution:

    x2 + √5x – 10 = 0
    x2 + 2√5x – √5x – 10 = 0
    Gives x = -2√5, √5
    2y2 + 9√5y + 50 = 0
    2y2 + 4√5y + 5√5y + 50 = 0
    Gives y = -2√5, -5√5/2
    Put all values on number line and analyze the relationship
    -5√5/2….. -2√5….. √5
  3. I. 2x2 – (8+√3)x + 4√3 = 0
    II. 3y2 – (6+2√3)y + 4√3 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    2x2 – (8+√3)x + 4√3 = 0
    By multiplying we have to 2*4√3 = 8√3 and by adding/subtracting we have to get – (8+√3)
    So factors are -8 and -√3
    So 2x2 – (8+√3)x + 4√3 = 0
    Gives
    2x2 – 8x – √3x + 4√3 = 0
    2x(x- 4) – √3(x – 4) = 0
    So x = 4, √3/2
    NEXT
    3y2 – (6+2√3)y + 4√3 = 0
    By multiplying we have to 3*4√3 = 12√3 and by adding/subtracting we have to get –(6+2√3)
    So factors are -6 and -2√3
    So 3y2 – (6+2√3)y + 4√3 = 0
    Gives
    3y2 – 6y – 2√3y + 4√3 = 0
    3y(y- 2) – 2√3(y – 2) = 0
    So x = 2, 2√3/3
    Put all values on number line and analyze the relationship
    √3/2…… 2√3/3…… 2… 4
  4. I. x2 – (2+√5)x + 2√5 = 0
    II. 2y2 – (6+3√5)y + 9√5 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B
    Solution:

    x2 – (2+√5)x + 2√5 = 0
    By multiplying we have to 2√5 and by adding/subtracting we have to get – (2+√5)
    So factors are -2 and -√5
    So x2 – (2+√5)x + 2√5 = 0
    Gives
    x2 – 2x – √5x + 2√5 = 0
    x(x- 2) – √5(x – 2) = 0
    So x = 2, √5
    NEXT
    2y2 – (6+3√5)y + 9√5 = 0
    By multiplying we have to 2*9√5 = 18√5 and by adding/subtracting we have to get –(6+3√5)
    So factors are -6 and -3√5
    So 2y2 – (6+3√5)y + 9√5 = 0
    Gives
    2y2 – 6y – 3√5y + 9√5 = 0
    2y(y- 3) – 3√5(y – 3) = 0
    So x = 3, 3√5/2
    Put all values on number line and analyze the relationship
    2…… √5…… 3… 3√5/2
  5. I. 3x2 + 5√2x – 24 = 0
    II. y2 – 6√2y + 16 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B
    Solution:

    3x2 + 5√2x – 24 = 0
    3x2 + 9√2x – 4√2x – 24 = 0
    Gives x = -3√2, 4√2/3
    y2 – 6√2y + 16 = 0
    y2 – 2√2y – 4√2y + 16 = 0
    Gives y = 2√2, 4√2
    Put all values on number line and analyze the relationship
    3√2……. 4√2/3…… 2√2….. 4√2
  6. I. 3x2 – 23x + 40 = 0
    II. 3y2 – 8y + 4 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option A
    Solution:

    3x2 – 23x + 40 = 0
    3x2 – 15x – 8x + 40 = 0
    Gives x = 5, 8/3
    3y2 – 8y + 4 = 0
    3y2 – 6y – 2y + 4 = 0
    Gives y = 2/3, 2
    Put all values on number line and analyze the relationship
    2/3….. 2….. 8/3….. 5
  7. I. 5x2 – 17x + 6 = 0
    II. 4y2 – 16y + 7 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    5x2 – 17x + 6 = 0
    5x2 – 15x – 2x + 6 = 0
    Gives x = 2/5, 3
    4y2 – 16y + 7 = 0
    4y2 – 2y – 14y + 7 = 0
    Gives y = 1/2, 7/2
    Put all values on number line and analyze the relationship
    2/5….. 1/2….. 3…. 7/2
  8. I. 3x2 – 14x + 8 = 0
    II. 3y2 – 20y + 12 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option E
    Solution:

    3x2 – 14x + 8 = 0
    3x2 – 12x – 2x + 8 = 0
    Gives x = 4, 2/3
    3y2 – 20y + 12 = 0
    3y2 – 18y – 2y + 12 = 0
    Gives y = 2/3, 6
    Put all values on number line and analyze the relationship
    2/3…….. 4….. 6
  9. I. 12x2 + 25x + 12 = 0
    II. 3y2 + 22y + 24 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option C
    Solution:

    12x2 + 25x + 12 = 0
    12x2 + 16x + 9x + 12 = 0
    Gives x = -4/3, -3/4
    3y2 + 22y + 24 = 0
    3y2 + 18y + 4y + 24 = 0
    Gives y = -4/3, -6
    Put all values on number line and analyze the relationship
    -6…… -4/3…… -3/4
  10. I. 6x2 + x – 2 = 0
    II. 3y2 – 22y + 40 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relation cannot be established
    View Answer
    Option B
    Solution:

    6x2 + x – 2 = 0
    6x2 + 4x – 3x – 2 = 0
    Gives x = 1/2, -2/3
    3y2 – 22y + 40 = 0
    3y2 – 12y – 10y + 40 = 0
    Gives y = 10/3, 4
    Put all values on number line and analyze the relationship
    -2/3…… 1/2…… 10/3….. 4

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