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Find the value of k such that the polynomial x2
-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product
? Related: Zeros of a Linear Polynomial
Most Upvoted Answer
Find the value of k such that the polynomial x2
-(k+6)
x+2(2k-1) has ...
Introduction:
In this problem, we are given a quadratic polynomial and we need to find the value of k such that the sum of its zeroes is equal to half of their product.
Quadratic Polynomial:
The given quadratic polynomial is x^2 - (k 6)x + 2k - 1
Sum and Product of Roots:
Let the roots of the quadratic polynomial be α and β.
Then, we know that:
α + β = -(coefficient of x)/coefficient of x^2 = (k 6)
αβ = constant term/coefficient of x^2 = 2k - 1
Equation:
We need to find the value of k such that the sum of the roots is equal to half of their product.
i.e., (α + β) = (1/2)αβ
Substituting the values of α + β and αβ, we get:
(k 6) = (1/2)(2k - 1)
2(k 6) = 2k - 1
2k - 12k + 6 = 0
k = 3
Conclusion:
Hence, the value of k such that the sum of the roots of the quadratic polynomial x^2 - (k 6)x + 2k - 1 is equal to half of their product is k = 3.
In this problem, we are given a quadratic polynomial and we need to find the value of k such that the sum of its zeroes is equal to half of their product.
Quadratic Polynomial:
The given quadratic polynomial is x^2 - (k 6)x + 2k - 1
Sum and Product of Roots:
Let the roots of the quadratic polynomial be α and β.
Then, we know that:
α + β = -(coefficient of x)/coefficient of x^2 = (k 6)
αβ = constant term/coefficient of x^2 = 2k - 1
Equation:
We need to find the value of k such that the sum of the roots is equal to half of their product.
i.e., (α + β) = (1/2)αβ
Substituting the values of α + β and αβ, we get:
(k 6) = (1/2)(2k - 1)
2(k 6) = 2k - 1
2k - 12k + 6 = 0
k = 3
Conclusion:
Hence, the value of k such that the sum of the roots of the quadratic polynomial x^2 - (k 6)x + 2k - 1 is equal to half of their product is k = 3.
Community Answer
Find the value of k such that the polynomial x2
-(k+6)
x+2(2k-1) has ...
k=7
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Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? 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 Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial?.
Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? 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 Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? covers all topics & solutions for Class 10 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Find the value of k such that the polynomial x2 -(k+6) x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial?.
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-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? in English & in Hindi are available as part of our courses for Class 10.
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-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? defined & explained in the simplest way possible. Besides giving the explanation of
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-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial?, a detailed solution for Find the value of k such that the polynomial x2
-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? has been provided alongside types of Find the value of k such that the polynomial x2
-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? theory, EduRev gives you an
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-(k+6)
x+2(2k-1) has sum of its zeroes equal to half of their product Related: Zeros of a Linear Polynomial? tests, examples and also practice Class 10 tests.
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