If the sum of zeroes of the quadratic polynomial 2x^2-(2k+1) x+(3k-1) is half of the product of its zeroes. Find value of k?

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If the sum of zeroes of the quadratic polynomial 2x^2-(2k+1) x+(3k-1) is half of the product of its zeroes. Find value of k?

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Julia 7 days 2021-10-09T05:53:38+00:00 1 Answer 0 views 0

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    2021-10-09T05:55:10+00:00

    K = -1/7

    Given :

    Quadratic polynomial 2x^2 (2k+1)x + (3k1)

    The sum of the zeroes of the above polynomial is equal to half of the product of its zeroes

    To find :

    Value of k

    Explanation :

    Let the zeroes be x and y , Then according to the quesion :

    x + y = 1/2 × xy

    Sum of the zeroes = x+y = -b / a = -2k-1/2

    b = (2k+1) = 2k1

    a = 2

    Product of the zeroes = xy = c / a = 3k1/2

    c = 3k1

    a = 2

    Putting the values :

    -2k 1/2 = 1/2 × 3k1/2

    -2k-1/2 = 3k1/4

    -2k-1 = 3k1/2

    -4k-2 = 3k1

    -4k-3k = 1+2

    -7k = 1

    k = 1/7

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