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x² – 20x + 84 = 0
y² – 24y + 135 = 0
- a)X > Y
- b)X < Y
- c)X ≥ Y
- d)X ≤ Y
- e)X = Y or relation cannot be established
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X...
x² – 20x + 84 = 0
x = 14, 6
y² – 24y + 135 = 0
y = 15, 9
x = 14, 6
y² – 24y + 135 = 0
y = 15, 9
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x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X...
Understanding the Quadratic Equations
To determine the relationship between X and Y, we first need to solve the given quadratic equations.
Equation for X
The first equation is:
- X² - 20X + 84 = 0
We can factor this equation:
- (X - 14)(X - 6) = 0
This gives us the solutions:
- X = 14 or X = 6
Equation for Y
The second equation is:
- Y² - 24Y + 135 = 0
Factoring this equation gives us:
- (Y - 15)(Y - 9) = 0
This results in:
- Y = 15 or Y = 9
Analyzing the Values
Now we have the possible values for X and Y:
- X can be either 14 or 6
- Y can be either 15 or 9
Let's compare these values:
- When X = 14:
- Y can be 15, thus X < y="" -="" when="" x="6:" -="" y="" can="" be="" 15="" or="" 9,="" thus="" x="" />< y="" in="" both="" cases.="" />Conclusion
From our analysis, we find that:
- X is less than Y in all scenarios.
However, since X can take two distinct values (6 and 14), and Y also has two distinct values (9 and 15), there are situations where X equals Y (if both are equal), but in the given cases, they cannot be equal.
Thus, the correct answer is:
Correct Answer: E - X = Y or relation cannot be established.
To determine the relationship between X and Y, we first need to solve the given quadratic equations.
Equation for X
The first equation is:
- X² - 20X + 84 = 0
We can factor this equation:
- (X - 14)(X - 6) = 0
This gives us the solutions:
- X = 14 or X = 6
Equation for Y
The second equation is:
- Y² - 24Y + 135 = 0
Factoring this equation gives us:
- (Y - 15)(Y - 9) = 0
This results in:
- Y = 15 or Y = 9
Analyzing the Values
Now we have the possible values for X and Y:
- X can be either 14 or 6
- Y can be either 15 or 9
Let's compare these values:
- When X = 14:
- Y can be 15, thus X < y="" -="" when="" x="6:" -="" y="" can="" be="" 15="" or="" 9,="" thus="" x="" />< y="" in="" both="" cases.="" />Conclusion
From our analysis, we find that:
- X is less than Y in all scenarios.
However, since X can take two distinct values (6 and 14), and Y also has two distinct values (9 and 15), there are situations where X equals Y (if both are equal), but in the given cases, they cannot be equal.
Thus, the correct answer is:
Correct Answer: E - X = Y or relation cannot be established.
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x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer?.
x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? for Quant 2026 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer? covers all topics & solutions for Quant 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x² – 20x + 84 = 0y² – 24y + 135 = 0a)X > Yb)X < Yc)X ≥ Yd)X ≤ Ye)X = Y or relation cannot be establishedCorrect answer is option 'E'. Can you explain this answer?.
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