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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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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\[(x-8)(x-k) = x^{2} -5kx + m\]
simplify the left side: x^2 - kx - 8x + 8k = x^2 - (k+8)x + 8k
x^2 - (k+8)x + 8k = x^2 - 5kx + m

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

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