# 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