Quantitative Aptitude

Quadratic Equations

367 Questions
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Quadratic Equations Questions

Multiple choice

In each question two equations numbered I and II are given. You have to solve both the equations and mark the appropriate answer. (I) 18x2+18x+4=0 (II) 12y2+29y+14=0

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. If x = y or no relation can be established between x and y.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Equation I: 18x^2 + 18x + 4 = 0 gives x = -1/3 or x = -2/3. Equation II: 12y^2 + 29y + 14 = 0 gives y = -4/3 or y = -7/4. Comparing: -1/3 > -4/3, -1/3 > -7/4, -2/3 > -4/3, -2/3 > -7/4. Therefore x ≥ y.

Multiple choice

$(x^2 = 256)$ $(y^2 + 18y + 17 = 0)$ On the basis of these equations, decide the relation between ‘x’ and ‘y’.
  1. $\(x > y\)$
  2. $\(x < y\)$
  3. $\(x \ge y\)$
  4. $\(x \le y\)$

  5. x = y or no relation can be established between x and y
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For x² = 256, x = ±16. For y² + 18y + 17 = 0, factoring gives (y+1)(y+17) = 0, so y = -1 or y = -17. When x = 16, x > y (both y values are negative). When x = -16, x > -17 but x < -1. Since x can be greater or less than y depending on the values, no single relation can be established. Option E is correct.

Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer.\newline I. (49x^{2} - 42x - 16 = 0)\newline II. (7y^{2} + 37y + 10 = 0)

  1. X > Y

  2. X < Y

  3. X ≤ Y

  4. X ≥ Y

  5. X = Y or the relationship can’t be established
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Solving equation I gives x = 8/7 and x = -2/7. Solving equation II gives y = -5 and y = -2/7. Comparing the values: 8/7 > -5, 8/7 > -2/7, -2/7 > -5, and -2/7 = -2/7. Since all x values are greater than or equal to all y values (with equality at one point), x ≥ y is correct.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find the relationship among them and give your answer as: $Quantity I: (x^2 = x) Quantity II: (2y^2 - y - 1 = 0)$

  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
E Correct answer
Explanation

Quantity I: x² = x gives x(x - 1) = 0, so 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. Both quantities can be 1, but x can also be 0 while y can be -0.5. No consistent relationship can be established. Option E is correct.

Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer.(I. x^2 + 9x + 20 = 0 ) (II. y^2 - 16 = 0)
  1. $\(x > y\)$
  2. $\(x < y\)$
  3. $\(x \le y\)$
  4. $\(x \ge y\)$

  5. X = Y or the relationship can’t be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solving equation I: x² + 9x + 20 = 0 gives x = -4, -5. Solving equation II: y² - 16 = 0 gives y = 4, -4. Comparing all values: x = -4 equals y = -4; in all other cases x is less than y. Therefore x ≤ y is always true.

Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equations and choose the correct answer.\newline I. (x^2 - x - 72 = 0)\newline II. (y^2 + y - 56 = 0)
  1. $\(x > y\)$
  2. $\(x < y\)$
  3. $\(x \le y\)$
  4. $\(x \ge y\)$
  5. $\(x = y\) or the relationship cannot be established$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation I: x² - x - 72 = 0 gives (x - 9)(x + 8) = 0, so x = 9 or x = -8. Solving equation II: y² + y - 56 = 0 gives (y + 8)(y - 7) = 0, so y = -8 or y = 7. Comparing values: x = 9 > y = -8, x = 9 > y = 7, x = 9 > y = -8, x = -8 = y = -8, x = -8 < y = 7. Since x is sometimes greater than, sometimes equal to, and sometimes less than y, the relationship cannot be established.

Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer.\newline I. (x^2 - 20x + 91 = 0)\newline II. (y^2 + 16y + 63 = 0)

  1. X > Y

  2. X < Y

  3. X ≤ Y

  4. X ≥ Y

  5. X = Y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation I: x² - 20x + 91 = 0 factors to (x-13)(x-7)=0, so x=13 or x=7. Equation II: y² + 16y + 63 = 0 factors to (y+7)(y+9)=0, so y=-7 or y=-9. Since all x values (13,7) are greater than all y values (-7,-9), X > Y.

Multiple choice

In each question two equations numbered I and II are given, you have to solve both the equation and choose the correct answer. I. x² + 9x + 20 = 0 II. 8y² – 15y + 7 = 0

  1. X > Y

  2. X < Y

  3. X ≤ Y

  4. X ≥ Y

  5. X = Y or the relationship cannot be established
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Equation I: x² + 9x + 20 = 0 factors to (x+4)(x+5)=0, so x=-4 or x=-5. Equation II: Using quadratic formula on 8y² - 15y + 7 = 0 gives y = (15 ± 1)/16, so y=1 or y=7/8. Since all x values (-4,-5) are less than all y values (1, 0.875), X < Y.

Multiple choice

In the following questions, two equations x and y are given. You have to solve both the equations and give answer. निम्नलिखित प्रश्नों में, दो समीकरणों के x और y दिए गए हैं। आपको दोनों समीकरणों को हल करना है और प्रश्न का उत्तर देना है। I. (41)2 – 1139 ÷ 67 = x × 64 II. y2 + y – 30 = 0

  1. x > y

  2. x ≥ y

  3. x <y

  4. x ≤ y

  5. x = y or the relation cannot be established x = y या संबंध स्थापित नहीं किया जा सकता या
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation I: (41)^2 - 1139 ÷ 67 = x × 64. 1681 - 17 = 64x, so 1664 = 64x, x = 25.875. Equation II: y² + y - 30 = 0. Factorizing: (y+6)(y-5) = 0, so y = 5 or y = -6. Comparing: x = 25.875 > y (both values of y are smaller). Therefore x > y.

Multiple choice

For each of the following pairs of equations find the relationship between m & n. दिये गये निम्न समीकरण युग्मों में x और y के बीच में संबंध ज्ञात कीजिए (I) 18x2 -5x - 2 = 0 (II) 2y2 -15y + 18 = 0

  1. If x > y If x > y

  2. If x < y If x < y

  3. If x ≥ y If x ≥ y

  4. If x ≤ y If x ≤ y

  5. If x = y or no relation between x and y can be established यदि x = y या x और y के मध्य कोई सम्बन्ध स्थापित नहीं किया जा सकता है |
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Solving 18x² - 5x - 2 = 0 gives x = 1/2 or x = -2/9. Solving 2y² - 15y + 18 = 0 gives y = 6 or y = 3/2. All possible x values (-2/9, 1/2) are less than all possible y values (3/2, 6), so x < y is always true.

Multiple choice

In each of the following questions, two equations I and II are given. You have to solve them and Give answer निम्नलिखित प्रश्नों में दो समीकरण I और II दिए गए हैं। इन दोनों को हल करके निम्नानुसार उत्तर दीजिए- 1. x3 – 15x = (20 – x) × 15 + 212 2. 2y2 – 13y + 15 = 0

  1. If x > y यदि x > y

  2. If x ≤ y यदि x ≤ y

  3. If x < y यदि x < y

  4. If x ≥ y यदि x ≥ y

  5. If x = y or relationship cannot be established यदि x = y या सम्बन्ध ज्ञात नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Equation I: x³ - 15x = (20 - x) × 15 + 212 simplifies to x³ - 15x = 300 - 15x + 212, giving x³ = 512, so x = 8. Equation II: 2y² - 13y + 15 = 0 gives (2y - 3)(y - 5) = 0, so y = 1.5 or y = 5. Since x = 8 > 1.5, 5, option A (x > y) is correct.

Multiple choice

In the followng questions two equations I and II are given. Solve both the equations and give answer निम्नलिखित प्रश्नों में दो समीकरण (I) और (II) दिये गये हैं दोनों समीकरण हल कीजिए और उत्तर दीजिए- (I) 2x2- 29x+105=0 (II) 2y2-15y+28=0

  1. If x>y यदिx>y

  2. If x≥y यदिx≥y

  3. If x<y यदिx<y

  4. If x ≤ y If x ≤ y

  5. If x=y or relation can not be established. संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving the first equation 2x² - 29x + 105 = 0 gives x = 15 or 3.5. Solving the second equation 2y² - 15y + 28 = 0 gives y = 7 or 2. When comparing the values, the minimum x value (3.5) is still greater than the minimum y value (2), and all x values are greater than all y values except at the point 3.5 = 3.5. However, since x can take value 15 which is greater than both y values, the relationship x > y holds.

Multiple choice

In each of the following questions, two equations (I) and (II) are given. You have to solve them and answer the given question. निम्नलिखित प्रश्नों में दो समीकरण (I) और (II) दिये गये हैं दोनों समीकरण हल कीजिए और प्रश्नों के उत्तर दीजिए। I. x2–24x+144=0 II. 2y2–52y+338=0

  1. If x>y If x>y

  2. If x≥y If x≥y

  3. If x<y If x<y

  4. If x≤y If x≤y

  5. If x=y or relationship cannot be established. यदि x=y या सम्बन्ध स्थापित नहीं किया जा सकता है।
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Equation I: x²-24x+144=0 is (x-12)²=0, so x=12. Equation II: 2y²-52y+338=0 can be written as y²-26y+169=0, which is (y-13)²=0, so y=13. Since 12 < 13, we have x < y.

Multiple choice

Find the correct relationship between given quantities. Quantity I: 2x2 + 29x+ 50 = 0 Quantity II: 3y2 + 18y+ 27 = 0 दी गई राशियों के बीच सही संबंध ज्ञात कीजिये। मात्रा I: 2x2 + 29x+ 50 = 0 मात्रा II: 3y2 + 18y+ 27 = 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 संबंध स्थापित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

For Quantity I: 2x² + 29x + 50 = 0 gives x = -25 or x = -2. For Quantity II: 3y² + 18y + 27 = 0 simplifies to y² + 6y + 9 = 0, which is (y+3)² = 0, giving y = -3. When x = -25, x < y. When x = -2, x > y. Since x can be less than or greater than y depending on which root we take, no definite relationship can be established.

Multiple choice

In the following questions two equations numbered I and II are given. You have to solve both the equation and give answer- निम्नलिखित प्रश्नों में दो समीकरण I और II दिए गये हैं। आपको दोनों समीकरण हल करने हैं और उत्तर दीजिए- I. 2x2+11x+12 = 0 II. 5y2+27y+10 = 0

  1. If x > y यदि x > y

  2. If x < y यदि x < y

  3. If x ≥ y यदि x ≥ y

  4. If x≤ y यदि x≤ y

  5. If x = y or relation can not be established यदि x = y or relation can not be established
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Solving equation I: 2x² + 11x + 12 = 0 gives x = -1.5 or x = -4. Solving equation II: 5y² + 27y + 10 = 0 gives y = -0.36 or y = -5.36. Since some x values are greater than some y values (-1.5 > -5.36) and some x values are less than some y values (-4 < -0.36), no clear relationship can be established.