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The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?
Correct answer is '56'. Can you explain this answer?
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The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean...
x2 - 49x + 600 = (x - 24) (x - 25) = 0
The Pythagorean triplet in 7, 24, 25.
The sum is 56.
Answer: 56
The Pythagorean triplet in 7, 24, 25.
The sum is 56.
Answer: 56
Most Upvoted Answer
The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean...
Finding the Roots of the Quadratic Equation
To solve the equation x² - 49x + 600 = 0, we can apply the quadratic formula:
x = [ -b ± √(b² - 4ac) ] / 2a
Here, a = 1, b = -49, and c = 600.
Calculating the Discriminant
- The discriminant (D) is calculated as follows:
- D = b² - 4ac = 49² - 4(1)(600)
- D = 2401 - 2400 = 1
Finding the Roots
- Now, substituting the values into the quadratic formula:
- x = [49 ± √1] / 2
- x = [49 ± 1] / 2
- The roots are:
- x₁ = (50) / 2 = 25
- x₂ = (48) / 2 = 24
Identifying the Pythagorean Triplet
- The roots 24 and 25 can form a Pythagorean triplet. A common triplet is (24, 25, 7).
- Here, 24² + 7² = 576 + 49 = 625 = 25².
Calculating the Sum of the Triplet
- The sum of the triplet (24, 25, 7) is:
- 24 + 25 + 7 = 56
Conclusion
The sum of the Pythagorean triplet that includes the roots of the quadratic equation is 56.
To solve the equation x² - 49x + 600 = 0, we can apply the quadratic formula:
x = [ -b ± √(b² - 4ac) ] / 2a
Here, a = 1, b = -49, and c = 600.
Calculating the Discriminant
- The discriminant (D) is calculated as follows:
- D = b² - 4ac = 49² - 4(1)(600)
- D = 2401 - 2400 = 1
Finding the Roots
- Now, substituting the values into the quadratic formula:
- x = [49 ± √1] / 2
- x = [49 ± 1] / 2
- The roots are:
- x₁ = (50) / 2 = 25
- x₂ = (48) / 2 = 24
Identifying the Pythagorean Triplet
- The roots 24 and 25 can form a Pythagorean triplet. A common triplet is (24, 25, 7).
- Here, 24² + 7² = 576 + 49 = 625 = 25².
Calculating the Sum of the Triplet
- The sum of the triplet (24, 25, 7) is:
- 24 + 25 + 7 = 56
Conclusion
The sum of the Pythagorean triplet that includes the roots of the quadratic equation is 56.
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The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer?
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The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer?.
The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The roots of the equation x2 - 49x + 600 = 0 are part of a Pythagorean triplet. What is the sum of that Pythagorean triplet?Correct answer is '56'. Can you explain this answer?.
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