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The zeroes of the quadratic polynomial x2 + 99x + 127 are
- a)both positive
- b)both negative
- c)one positive and one negative
- d)both equal
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiv...
Given quadratic polynomial is x2 + 99x + 127.
By comparing with the standard form, we get;
a = 1, b = 99 and c = 127
a > 0, b > 0 and c > 0
We know that in any quadratic polynomial, if all the coefficients have the same sign, then the zeroes of that polynomial will be negative.
Therefore, the zeroes of the given quadratic polynomial are negative.
Most Upvoted Answer
The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiv...
Understanding the Quadratic Polynomial
The given quadratic polynomial is x² + 99x + 127. To determine the nature of its roots (zeroes), we can use the properties of quadratic equations.
Roots of a Quadratic Equation
The roots of the polynomial can be found using the formula:
x = [-b ± √(b² - 4ac)] / 2a,
where a = 1, b = 99, and c = 127.
Discriminant Analysis
To analyze the nature of the roots, we look at the discriminant (D):
D = b² - 4ac = 99² - 4(1)(127).
Calculating the discriminant:
- 99² = 9801
- 4 * 1 * 127 = 508
- Therefore, D = 9801 - 508 = 9293.
Nature of the Roots
Now, let's evaluate the discriminant:
- Since D > 0, the quadratic has two distinct real roots.
Sum and Product of Roots
Using Vieta's formulas:
- The sum of the roots (α + β) = -b/a = -99.
- The product of the roots (αβ) = c/a = 127.
Evaluation of Roots
1. Sum of Roots:
- Since the sum is negative (-99), at least one of the roots must be negative.
2. Product of Roots:
- The product is positive (127), meaning both roots must be either positive or negative.
Since the sum is negative and the product is positive, it confirms that both roots must be negative.
Conclusion
Thus, the correct answer is option B: both negative.
The given quadratic polynomial is x² + 99x + 127. To determine the nature of its roots (zeroes), we can use the properties of quadratic equations.
Roots of a Quadratic Equation
The roots of the polynomial can be found using the formula:
x = [-b ± √(b² - 4ac)] / 2a,
where a = 1, b = 99, and c = 127.
Discriminant Analysis
To analyze the nature of the roots, we look at the discriminant (D):
D = b² - 4ac = 99² - 4(1)(127).
Calculating the discriminant:
- 99² = 9801
- 4 * 1 * 127 = 508
- Therefore, D = 9801 - 508 = 9293.
Nature of the Roots
Now, let's evaluate the discriminant:
- Since D > 0, the quadratic has two distinct real roots.
Sum and Product of Roots
Using Vieta's formulas:
- The sum of the roots (α + β) = -b/a = -99.
- The product of the roots (αβ) = c/a = 127.
Evaluation of Roots
1. Sum of Roots:
- Since the sum is negative (-99), at least one of the roots must be negative.
2. Product of Roots:
- The product is positive (127), meaning both roots must be either positive or negative.
Since the sum is negative and the product is positive, it confirms that both roots must be negative.
Conclusion
Thus, the correct answer is option B: both negative.
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The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer?.
The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer? for Class 10 2025 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The zeroes of the quadratic polynomial x2+ 99x + 127 area)both positiveb)both negativec)one positive and one negatived)both equalCorrect answer is option 'B'. Can you explain this answer?.
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