(x-8)(x-k) = x^2 - 5kx +m. In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?

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24-07-2016
Mathematics

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(x-8)(x-k) = x^2 - 5kx +m. In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?

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konrad509 konrad509 · Answer 1 · 2016-07-24T13:09:08+02:00

konrad509 konrad509

24-07-2016

[tex](x-8)(x-k) = x^2 - 5kx +m\\ x^2-kx-8x+8k=x^2 - 5kx +m\\ x^2-(k+8)x+8k=x^2 - 5kx +m\\\\ -(k+8)=-5k\\8k=m\\\\ -(k+8)=-5k\\ -k-8=-5k\\ 4k=8\\ k=2\\\\ m=8\cdot2\\ \boxed{m=16} [/tex]

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