the roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.​

Question

the roots of the equation x²-kx+28=0 are alpha (a) and alpha (a) + 3.find the values of k.​

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Amara 1 month 2021-10-21T00:00:35+00:00 1 Answer 0 views 0

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    2021-10-21T00:02:17+00:00

    The possible values of k are -11 and 11

    Solution:

    Given that equation is:

    x^2 - kx + 28 = 0

    Roots are:

    \alpha\\\\\alpha + 3

    To find: value of x

    The general quadratic equation is:

    ax^2 + bx + c = 0

    \text{ Product of roots } = \frac{c}{a}\\\\\text{ Sum of roots } = \frac{-b}{a}

    From given,

    x^2 - kx + 28 = 0

    a = 1

    b = -k

    c = 28

    Therefore,

    Product\ of\ roots = \frac{28}{1} = 28

    Sum\ of\ roots = \frac{-k}{1} = -k

    Given roots are:

    \alpha\\\\\alpha + 3

    Therefore,

    The two roots are two numbers whose difference is 3 and whose product is 28

    Those two roots are 4 and 7 or -4 and -7

    Then, sum of roots are:

    4 + 7 = 11

    -4 – 7 = -11

    Therefore, the possible values of k are -11 and 11

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