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Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively?
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Find a quadratic polynomial where dum and product of its zeroes are 0,...
Quadratic Polynomial with Zeroes 0 and √7
To find a quadratic polynomial with zeroes 0 and √7, we can use the fact that the sum and product of the zeroes of a quadratic polynomial are related to its coefficients.
Sum and Product of Zeroes
- The sum of the zeroes of a quadratic polynomial ax^2 + bx + c is given by -b/a.
- The product of the zeroes of the quadratic polynomial is given by c/a.
Given that the sum of the zeroes is 0 and the product of the zeroes is √7, we have:
- Sum of zeroes = -b/a = 0
- Product of zeroes = c/a = √7
Finding the Quadratic Polynomial
Since the sum of the zeroes is 0, we can see that b = 0.
Now, we can substitute b = 0 into the product of zeroes equation:
c/a = √7
c = a√7
Therefore, the quadratic polynomial with zeroes 0 and √7 can be written as:
f(x) = a(x - 0)(x - √7)
f(x) = a(x)(x - √7)
f(x) = ax^2 - a√7x
This quadratic polynomial satisfies the given conditions of having zeroes 0 and √7.
To find a quadratic polynomial with zeroes 0 and √7, we can use the fact that the sum and product of the zeroes of a quadratic polynomial are related to its coefficients.
Sum and Product of Zeroes
- The sum of the zeroes of a quadratic polynomial ax^2 + bx + c is given by -b/a.
- The product of the zeroes of the quadratic polynomial is given by c/a.
Given that the sum of the zeroes is 0 and the product of the zeroes is √7, we have:
- Sum of zeroes = -b/a = 0
- Product of zeroes = c/a = √7
Finding the Quadratic Polynomial
Since the sum of the zeroes is 0, we can see that b = 0.
Now, we can substitute b = 0 into the product of zeroes equation:
c/a = √7
c = a√7
Therefore, the quadratic polynomial with zeroes 0 and √7 can be written as:
f(x) = a(x - 0)(x - √7)
f(x) = a(x)(x - √7)
f(x) = ax^2 - a√7x
This quadratic polynomial satisfies the given conditions of having zeroes 0 and √7.
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Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively?
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Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively?.
Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find a quadratic polynomial where dum and product of its zeroes are 0,√7 respectively?.
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