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Given below are two quantities named A and B. Based on the information, you have to determine the relation between two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.
Quantity A: 4x2 – 29x + 45 = 0
Quantity B: 3y2 – 19y + 28 = 0
Quantity A: 4x2 – 29x + 45 = 0
Quantity B: 3y2 – 19y + 28 = 0
- a)Quantity A > Quantity B
- b)Quantity A < Quantity B
- c)Quantity A ≥ Quantity B
- d)Quantity A ≤ Quantity B
- e)Quantity A = Quantity B or Relationship can’t be established
Correct answer is option 'E'. Can you explain this answer?
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Most Upvoted Answer
Given below are two quantities named A and B. Based on the information...
Understanding the Quadratic Equations
To compare Quantity A and Quantity B, we need to analyze the given quadratic equations.
Quantity A: 4x² – 29x + 45 = 0
- This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \).
- Here, \( a = 4 \), \( b = -29 \), and \( c = 45 \).
- We can find the roots using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Calculating the discriminant \( D \):
- \( D = b^2 - 4ac = (-29)^2 - 4(4)(45) = 841 - 720 = 121 \).
Since \( D > 0 \), Quantity A has two real and distinct roots.
Quantity B: 3y² – 19y + 28 = 0
- This equation is also in the form \( ay^2 + by + c = 0 \).
- Here, \( a = 3 \), \( b = -19 \), and \( c = 28 \).
- Again, using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Calculating the discriminant \( D \):
- \( D = (-19)^2 - 4(3)(28) = 361 - 336 = 25 \).
Since \( D > 0 \), Quantity B also has two real and distinct roots.
Conclusion on Relationship
- Both quantities represent quadratic equations that have real and distinct roots.
- However, without specific values for \( x \) and \( y \), we cannot definitively establish a numerical relationship between the two quantities.
- Thus, the correct answer is (E): Quantity A = Quantity B or Relationship can't be established.
This indicates that while both equations have solutions, their specific values are independent, leading to no definitive relationship.
To compare Quantity A and Quantity B, we need to analyze the given quadratic equations.
Quantity A: 4x² – 29x + 45 = 0
- This is a quadratic equation in standard form \( ax^2 + bx + c = 0 \).
- Here, \( a = 4 \), \( b = -29 \), and \( c = 45 \).
- We can find the roots using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Calculating the discriminant \( D \):
- \( D = b^2 - 4ac = (-29)^2 - 4(4)(45) = 841 - 720 = 121 \).
Since \( D > 0 \), Quantity A has two real and distinct roots.
Quantity B: 3y² – 19y + 28 = 0
- This equation is also in the form \( ay^2 + by + c = 0 \).
- Here, \( a = 3 \), \( b = -19 \), and \( c = 28 \).
- Again, using the quadratic formula \( y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Calculating the discriminant \( D \):
- \( D = (-19)^2 - 4(3)(28) = 361 - 336 = 25 \).
Since \( D > 0 \), Quantity B also has two real and distinct roots.
Conclusion on Relationship
- Both quantities represent quadratic equations that have real and distinct roots.
- However, without specific values for \( x \) and \( y \), we cannot definitively establish a numerical relationship between the two quantities.
- Thus, the correct answer is (E): Quantity A = Quantity B or Relationship can't be established.
This indicates that while both equations have solutions, their specific values are independent, leading to no definitive relationship.
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Community Answer
Given below are two quantities named A and B. Based on the information...
In quantity A
⇒ 4x2 – 29x + 45 = 0
⇒ 4x2 – 20x – 9x + 45 = 0
⇒ 4x (x – 5) -9 (x – 5) = 0
⇒ (4x – 9) (x – 5) = 0
⇒ X = 9/4, 5
In quantity B
⇒ 3y2 – 19y + 28 = 0
⇒ 3y2 – 12y – 7y + 28 = 0
⇒ 3y (y – 4) -7 (y – 4) = 0
⇒ (3y – 7) (y – 4) = 0
⇒ y = 7/3, 4
⇒ when x = 9/4, y = 7/3 then x < y
⇒ when x = 9/4, y = 4 then x < y
⇒ when x = 5, y = 7/3 then x > y
⇒ when x = 5, y = 4 then x > y
∴ Relation cannot be established
⇒ 4x2 – 29x + 45 = 0
⇒ 4x2 – 20x – 9x + 45 = 0
⇒ 4x (x – 5) -9 (x – 5) = 0
⇒ (4x – 9) (x – 5) = 0
⇒ X = 9/4, 5
In quantity B
⇒ 3y2 – 19y + 28 = 0
⇒ 3y2 – 12y – 7y + 28 = 0
⇒ 3y (y – 4) -7 (y – 4) = 0
⇒ (3y – 7) (y – 4) = 0
⇒ y = 7/3, 4
⇒ when x = 9/4, y = 7/3 then x < y
⇒ when x = 9/4, y = 4 then x < y
⇒ when x = 5, y = 7/3 then x > y
⇒ when x = 5, y = 4 then x > y
∴ Relation cannot be established
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Given below are two quantities named A and B. Based on the information, you have to determine the relation between two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.Quantity A: 4x2– 29x + 45 = 0Quantity B: 3y2– 19y + 28 = 0a)Quantity A > Quantity Bb)Quantity A < Quantity Bc)Quantity A ≥ Quantity Bd)Quantity A ≤ Quantity Be)Quantity A = Quantity B or Relationship can’t be establishedCorrect answer is option 'E'. Can you explain this answer?
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