Math- Equation solving for k?

Find the values of k for which the equation x^2 + k + 6 = kx +3x has equal roots

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  • 7 years ago
    Favorite Answer

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    x^2 + k + 6 = kx +3x

    x^2 -x(k+3) + (k+6) = 0

    The equation will have equal roots only if the polynomial is a perfect square. That happens when the discriminant is zero. So, solve

    (k+3)^2 - 4(k +6) = 0

    k^2 + 6k + 9 - 4k - 24 = 0

    k^2 + 2k - 15 = 0

    (k+5)(k-3) = 0

    k = -5 or k = 3 <--- answer

    ==

    Check

    When k = -5

    x^2 - x(-5 + 3) + (-5 + 6) = 0

    x^2 -2x + 1 = 0

    (x-1)^2 = 0 <--- equal roots

    When k = 3

    x^ - x(3+3) + (3+6) = 0

    x -6x + 9 = 0

    (x-3)^2 = 0 <--- equal roots

  • 3 years ago

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