SAT algebra

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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?

  • SAT algebra -

    (x-8)(x-k) = x^2-5kx+m
    x^2 - kx - 8x + 8k = x^2 - 5kx + m
    x^2 - x(k + 8) + 8k = x^2 - 5kx + m

    for the equation to be true
    -x(k+8) = -5kx and 8k = m
    k+8 = -5k and m = 8k
    6k =-8
    k = -4/3

    then m = 8(-4/3) = -32/3

  • SAT algebra -

    -x(k+8)=-5kx then why not k+8=5k => k=2 and m=16. why it is k+8=-5k. thought answere was 16. I did not have ansewer choice of -32/3 in the book.

  • SAT algebra -

    yeah, don't pay attention to original answerer... they are totally wrong.

    i'm looking for help too :|

  • SAT algebra -

    Reiny was right until 4th line up from the bottom. when you divide -x out, the equation should read k+8=+5k, not negative. thus, k would become 2, not -4/3 which leads us to m= 16

  • SAT algebra -

    x^2 -x(k+8)+8k=x^2-5kx+m

    let x(k+8) equivalent to 5kx & let 8k equivalent to m...

    (x(k+8))/x=(5kx)x
    x crosses out so
    k+8=5k....
    8=5k-k
    8=4k
    2=k

    if 8k=m then 8(2)=m
    16=m

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