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3psilon

  • 2 years ago

SAT help ? In the equation, 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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  1. 3psilon
    • 2 years ago
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    \[(x-8)(x-k) = x^{2} -5kx + m\]

  2. bahrom7893
    • 2 years ago
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    simplify the left side: x^2 - kx - 8x + 8k = x^2 - (k+8)x + 8k

  3. bahrom7893
    • 2 years ago
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    x^2 - (k+8)x + 8k = x^2 - 5kx + m

  4. bahrom7893
    • 2 years ago
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    thus you know that k+8 = 5k

  5. bahrom7893
    • 2 years ago
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    and 8k = m

  6. robinfr93
    • 2 years ago
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    just what bahrom said

  7. bahrom7893
    • 2 years ago
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    Now just solve for both.

  8. robinfr93
    • 2 years ago
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    bahrom mate can ya help me out with a sum of my own??

  9. robinfr93
    • 2 years ago
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    @bahrom7893

  10. bahrom7893
    • 2 years ago
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    @robinfr93 let me see the question

  11. 3psilon
    • 2 years ago
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    @bahrom7893 What does it mean by true for all values of x?

  12. 3psilon
    • 2 years ago
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    I don't see how you got k+8 = 5k Where did everything else go?

  13. bahrom7893
    • 2 years ago
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    it just means equate the two equations.

  14. bahrom7893
    • 2 years ago
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    I'm equating the coefficients: x^2 - (k+8)x + 8k = x^2 - 5kx + m

  15. bahrom7893
    • 2 years ago
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    |dw:1347995814720:dw|

  16. bahrom7893
    • 2 years ago
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    |dw:1347995848017:dw|

  17. bahrom7893
    • 2 years ago
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    for those two equations to be equal to each other for all x, k+8 has to equal 5k and 8k must equal m

  18. 3psilon
    • 2 years ago
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    Could it go the other way around? Like (k+8) = m? @bahrom7893

  19. bahrom7893
    • 2 years ago
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    No it couldn't, since x coefficients have to equal to corresponding x coefficients

  20. bahrom7893
    • 2 years ago
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    k+8 is coefficient of x^1, and so is 5k both 8k and m are coefficients of x^0

  21. 3psilon
    • 2 years ago
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    Ohhhh I see now ok ok thanks

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