3psilon
  • 3psilon
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?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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3psilon
  • 3psilon
\[(x-8)(x-k) = x^{2} -5kx + m\]
bahrom7893
  • bahrom7893
simplify the left side: x^2 - kx - 8x + 8k = x^2 - (k+8)x + 8k
bahrom7893
  • bahrom7893
x^2 - (k+8)x + 8k = x^2 - 5kx + m

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bahrom7893
  • bahrom7893
thus you know that k+8 = 5k
bahrom7893
  • bahrom7893
and 8k = m
anonymous
  • anonymous
just what bahrom said
bahrom7893
  • bahrom7893
Now just solve for both.
anonymous
  • anonymous
bahrom mate can ya help me out with a sum of my own??
anonymous
  • anonymous
@bahrom7893
bahrom7893
  • bahrom7893
@robinfr93 let me see the question
3psilon
  • 3psilon
@bahrom7893 What does it mean by true for all values of x?
3psilon
  • 3psilon
I don't see how you got k+8 = 5k Where did everything else go?
bahrom7893
  • bahrom7893
it just means equate the two equations.
bahrom7893
  • bahrom7893
I'm equating the coefficients: x^2 - (k+8)x + 8k = x^2 - 5kx + m
bahrom7893
  • bahrom7893
|dw:1347995814720:dw|
bahrom7893
  • bahrom7893
|dw:1347995848017:dw|
bahrom7893
  • bahrom7893
for those two equations to be equal to each other for all x, k+8 has to equal 5k and 8k must equal m
3psilon
  • 3psilon
Could it go the other way around? Like (k+8) = m? @bahrom7893
bahrom7893
  • bahrom7893
No it couldn't, since x coefficients have to equal to corresponding x coefficients
bahrom7893
  • bahrom7893
k+8 is coefficient of x^1, and so is 5k both 8k and m are coefficients of x^0
3psilon
  • 3psilon
Ohhhh I see now ok ok thanks

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