Class 10 Exam > Class 10 Questions > If 2 and (- 1/2)as the sum and product of its...
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If 2 and (- 1/2) as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –
- a)x2 – 2x – 4
- b)4x2 – 2x + 1
- c)2x2 + 4x – 1
- d)2x2 – 4x – 1
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
If 2 and (- 1/2)as the sum and product of its zeros respectively then ...
Understanding Quadratic Polynomials
A quadratic polynomial can be expressed in the form f(x) = ax² + bx + c, where the zeros (roots) of the polynomial can be derived from its coefficients.
Given Conditions
- Sum of Zeros (α + β): 2
- Product of Zeros (αβ): -1/2
Using the Relationships
For a quadratic polynomial f(x) = ax² + bx + c:
- The sum of the zeros is given by -b/a.
- The product of the zeros is given by c/a.
Using the conditions:
1. Sum of Zeros:
- -b/a = 2
- Therefore, b = -2a
2. Product of Zeros:
- c/a = -1/2
- Therefore, c = -a/2
Forming the Polynomial
Substituting b and c into the polynomial form:
f(x) = ax² + (-2a)x + (-a/2)
To eliminate the fraction, multiply through by 2:
f(x) = 2ax² - 4ax - a
Assuming a = 1 for simplicity:
f(x) = 2x² - 4x - 1
Thus, the polynomial becomes:
Final Polynomial
- f(x) = 2x² - 4x - 1
This corresponds to option D.
Conclusion
The correct quadratic polynomial based on the provided sum and product of its zeros is:
- 2x² - 4x - 1 (Option D)
A quadratic polynomial can be expressed in the form f(x) = ax² + bx + c, where the zeros (roots) of the polynomial can be derived from its coefficients.
Given Conditions
- Sum of Zeros (α + β): 2
- Product of Zeros (αβ): -1/2
Using the Relationships
For a quadratic polynomial f(x) = ax² + bx + c:
- The sum of the zeros is given by -b/a.
- The product of the zeros is given by c/a.
Using the conditions:
1. Sum of Zeros:
- -b/a = 2
- Therefore, b = -2a
2. Product of Zeros:
- c/a = -1/2
- Therefore, c = -a/2
Forming the Polynomial
Substituting b and c into the polynomial form:
f(x) = ax² + (-2a)x + (-a/2)
To eliminate the fraction, multiply through by 2:
f(x) = 2ax² - 4ax - a
Assuming a = 1 for simplicity:
f(x) = 2x² - 4x - 1
Thus, the polynomial becomes:
Final Polynomial
- f(x) = 2x² - 4x - 1
This corresponds to option D.
Conclusion
The correct quadratic polynomial based on the provided sum and product of its zeros is:
- 2x² - 4x - 1 (Option D)
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Community Answer
If 2 and (- 1/2)as the sum and product of its zeros respectively then ...
Given that the sum of the zeros is 2 and the product is 4, the quadratic equation has the form:
f(x) = a(x2 - 2x + 4)
Setting a = 2 (to match the coefficients), we get:
f(x) = 2(x2 - 2x + 4) = 2x2 - 4x - 1
So, the correct answer is:
d) 2x2 - 4x - 1.
f(x) = a(x2 - 2x + 4)
Setting a = 2 (to match the coefficients), we get:
f(x) = 2(x2 - 2x + 4) = 2x2 - 4x - 1
So, the correct answer is:
d) 2x2 - 4x - 1.
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If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct 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 If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct 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 If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer?.
If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct 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 If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct 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 If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer?.
Solutions for If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 10.
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If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of If 2 and (- 1/2)as the sum and product of its zeros respectively then the quadratic polynomial f(x) is –a)x2– 2x – 4b)4x2– 2x + 1c)2x2+ 4x – 1d)2x2– 4x – 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an
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