Class 10 Exam > Class 10 Questions > If sum of the zeroes of the polynomial is 4 a...
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If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial is
- a)x2 – 2x + 2
- b)x2 – 4x + 4
- c)x2 + 4x + 4
- d)x2 + 2x + 2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If sum of the zeroes of the polynomial is 4 and their product is 4, th...
Sum of zeros= α+β =4
Product of zeros=αβ=4
We have Quadratic equation as
x2-(Sum of zeros)x+Product of zeros
=x2-4x+4
Product of zeros=αβ=4
We have Quadratic equation as
x2-(Sum of zeros)x+Product of zeros
=x2-4x+4
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Community Answer
If sum of the zeroes of the polynomial is 4 and their product is 4, th...
Explanation:
- Let the quadratic polynomial be ax^2 + bx + c.
- According to the problem, the sum of the zeroes is 4.
- Let the zeroes be p and q.
- Therefore, p + q = 4.
- Also, according to the problem, their product is 4.
- Therefore, p * q = 4.
- Using the sum and product of the roots formulae, we can write:
- p + q = -b/a
- p * q = c/a
- Substituting the given values, we get:
- -b/a = 4
- c/a = 4
- Multiplying the second equation by -1, we get:
- -c/a = -4
- Substituting these values in the quadratic polynomial, we get:
- ax^2 + bx + c = ax^2 + 4ax + 4a (from the first equation)
- ax^2 + bx + c = ax^2 - 4a (from the second and third equations)
- Comparing the coefficients of x in both equations, we get:
- b = 4a
- b = 0 (since the coefficient of x is 0 in the second equation)
- Therefore, we get:
- 4a = 0
- a = 0
- Substituting the value of a in any of the two equations, we get:
- b = 0
- c = 4a
- c = 0
- Therefore, the quadratic polynomial is x^2 + 4x + 4, which is option B.
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If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct 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 If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct 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 If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct answer is option 'B'. Can you explain this answer?.
If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct 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 If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct 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 If sum of the zeroes of the polynomial is 4 and their product is 4, then the quadratic polynomial isa)x2– 2x + 2b)x2– 4x + 4c)x2+ 4x + 4d)x2+ 2x + 2Correct answer is option 'B'. Can you explain this answer?.
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