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The number of polynomials having zeroes as -2 and 5 is:
- a)1
- b)2
- c)3
- d)More than 3
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
The number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More...
The polynomials x2-3x-10, 2x2-6x-20, (1/2)x2-(3/2)x-5, 3x2-9x-30, have zeroes as -2 and 5.
Most Upvoted Answer
The number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More...
Understanding the Problem
The problem states that we need to find the number of polynomials that have -2 and 5 as their zeros. A polynomial can be expressed in terms of its roots.
Forming the Polynomial
The general form of a polynomial with given roots can be represented as:
- If p(x) is a polynomial with roots r1 and r2, then p(x) can be expressed as:
- p(x) = k(x + 2)(x - 5)
Here, -2 and 5 are the roots, and k is a non-zero constant that can take any real value.
Variability of the Polynomial
- The value of k can be any real number (positive, negative, or zero).
- Different values of k will yield different polynomials.
Examples of Polynomials
- If k = 1, then the polynomial is:
- p(x) = (x + 2)(x - 5) = x^2 - 3x - 10
- If k = -1, then:
- p(x) = -(x + 2)(x - 5) = -x^2 + 3x + 10
- If k = 2, then:
- p(x) = 2(x + 2)(x - 5) = 2x^2 - 6x - 20
Conclusion
Since k can take an infinite number of values, there are infinitely many polynomials that can be formed with -2 and 5 as zeros. Thus, the correct answer is:
- More than 3 (Option D).
The problem states that we need to find the number of polynomials that have -2 and 5 as their zeros. A polynomial can be expressed in terms of its roots.
Forming the Polynomial
The general form of a polynomial with given roots can be represented as:
- If p(x) is a polynomial with roots r1 and r2, then p(x) can be expressed as:
- p(x) = k(x + 2)(x - 5)
Here, -2 and 5 are the roots, and k is a non-zero constant that can take any real value.
Variability of the Polynomial
- The value of k can be any real number (positive, negative, or zero).
- Different values of k will yield different polynomials.
Examples of Polynomials
- If k = 1, then the polynomial is:
- p(x) = (x + 2)(x - 5) = x^2 - 3x - 10
- If k = -1, then:
- p(x) = -(x + 2)(x - 5) = -x^2 + 3x + 10
- If k = 2, then:
- p(x) = 2(x + 2)(x - 5) = 2x^2 - 6x - 20
Conclusion
Since k can take an infinite number of values, there are infinitely many polynomials that can be formed with -2 and 5 as zeros. Thus, the correct answer is:
- More than 3 (Option D).
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Community Answer
The number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More...
Correct answer is D
as polynomial =K[x^2-(sum of zeroes)x+product of zeroes]
And we can put any value of K
which means there are numerous number of polynomial with defined zeroes.
as polynomial =K[x^2-(sum of zeroes)x+product of zeroes]
And we can put any value of K
which means there are numerous number of polynomial with defined zeroes.
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The number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. 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 number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. 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 number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. Can you explain this answer?.
The number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. 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 number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. 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 number of polynomials having zeroes as -2 and 5 is:a)1b)2c)3d)More than 3Correct answer is option 'D'. Can you explain this answer?.
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