Quantitative Aptitude

Quadratic Equations

367 Questions
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Quadratic Equations Questions

Multiple choice

Directions: In this question, two equations (I) and (II) are given. You have to solve both the equations and give answer I. 25x2 - 30x - 27 = 0 II. 25y2 + 60y + 27 = 0

  1. x > y

  2. x ≥ y

  3. x < y

  4. x ≤ y

  5. x = y or the relationship between x and y cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 25x^2 - 30x - 27 = 0 gives roots x = 1.8 and x = -0.6. Solving 25y^2 + 60y + 27 = 0 gives roots y = -0.6 and y = -1.8. Comparing the sets, x >= y holds true for all combinations.

Multiple choice

Passage

In the given questions, two quantities are given, one as ‘Quantity 1’ and another as ‘Quantity 2’. You have to determine relationship between two quantities and choose the appropriate option:

Quantity I: x2 - 17x + 72 = 0. Find the value of x? Quantity II: y2 -13y + 40 =0. Find the value of y?

  1. Quantity I> Quantity II

  2. Quantity I< Quantity II

  3. Quantity II ≥ Quantity I

  4. Quantity II ≤ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Quantity I: x² - 17x + 72 = 0 factors to (x-8)(x-9) = 0, so x = 8 or 9. Quantity II: y² - 13y + 40 = 0 factors to (y-8)(y-5) = 0, so y = 8 or 5. Comparing values: x can be 8 or 9, y can be 8 or 5. When both are 8, they're equal; otherwise, x > y (9 > 8, 9 > 5, 8 > 5). So Quantity II ≤ Quantity I is correct.

Multiple choice

Passage

Each question below contains a statement followed by Quantity I and Quantity II. Find the relationship among them and give your answer as, नीचे दिए गए प्रत्येक प्रश्न में एक कथन है, जिसके बाद मात्रा I और मात्रा II हैं, उनके बीच संबंध ज्ञात कीजिये और अपना उत्तर दें।

Quantity I: x2=x Quantity II: 2y2-y-1=0 मात्रा I: x2=x मात्रा II: 2y2-y-1=0

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II ≥ Quantity I मात्रा II ≥ मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: x² = x gives x² - x = 0, so x(x-1) = 0, meaning x = 0 or x = 1. Quantity II: 2y² - y - 1 = 0 factors to (2y+1)(y-1) = 0, so y = -0.5 or y = 1. Testing all combinations: when x=0, y=-0.5 gives x>y; when x=0, y=1 gives xy; when x=1, y=1 gives x=y. No consistent relationship exists.

Multiple choice

Passage

Each question below contains a statement followed by Quantity I and Quantity II. Find the relationship among them and give your answer as,

Quantity I: x2=x Quantity II: 2y2-y-1=0

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I< Quantity II

  4. Quantity II ≤ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Quantity I: x² = x → x(x-1) = 0 → x = 0 or 1. Quantity II: 2y² - y - 1 = 0. Factorizing: (2y+1)(y-1) = 0 → y = -0.5 or 1. Since x can be 0 or 1, and y can be -0.5 or 1, the relationship varies: when x=0, x>y if y=-0.5 but xy if y=-0.5. No unique relation can be established.

Multiple choice

Passage

Directions: The question statement is followed by two quantities i.e. Quantity I and Quantity II. Select the option from given answer choices which reflects correct relationship between Quantity I and Quantity II as per the calculations based on question statement/s.

It is given that 4m + 12 x 162m – 12 = 643m – 20 and n2 – 30n + 216 = 0 Quantity I: Value of 'n'. Quantity II: Value of 'm'.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or cannot be calculated
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For the first equation, 4^(m+12) * 16^(2m-12) = 64^(3m-20) becomes 2^(2m+24) * 2^(8m-48) = 2^(18m-120). Equating exponents: 10m - 24 = 18m - 120, so 8m = 96, m = 12. For the second equation, n^2 - 30n + 216 = 0 factors to (n-12)(n-18) = 0, so n = 12 or 18. Comparing n and m: if n=12, n=m; if n=18, n>m. Thus n >= m.

Multiple choice

Passage

Q56_Q60(212975)Canara_1543821686_hindi.html

Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and give answer accordingly. Mark your answer as I. x2 - 15x + 50 = -4 II. y2 - 21y + 96 = -12

  1. if x > y

  2. if x ≥ y

  3. if x < y

  4. if x ≤ y

  5. if x = y, or the relationship cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I: x^2 - 15x + 54 = 0 -> (x-6)(x-9)=0 -> x=6, 9. II: y^2 - 21y + 108 = 0 -> (y-9)(y-12)=0 -> y=9, 12. Comparing sets: 6 < 9, 6 < 12, 9 = 9, 9 < 12. Thus x <= y.

Multiple choice

Passage

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Directions: In the following question, two equations (I) and (II) are given. You have to solve both the equations and give answer according to the following codes: I. 3x2 + 7x - 6 = 0 II. y(y + 6) = -9

  1. if x > y

  2. if x < y

  3. if x ≤ y

  4. if x ≥ y

  5. if x = y or relation cannot be established between x and y
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving (I) 3x^2 + 7x - 6 = 0 gives (3x-2)(x+3)=0, so x = 2/3 or -3. Solving (II) y^2 + 6y + 9 = 0 gives (y+3)^2 = 0, so y = -3. Comparing the roots, x is either 2/3 (which is > -3) or -3 (which is = -3). Thus, x >= y.