<p>Practice Test #3 in the BB, Section 5 #8</p>
<p>(x-8)(x-k) = x^2-5kx+m</p>
<p>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?</p>
<p>I guess - </p>
<p>you can get (m-8k)x = 4k-8, I’m sure. Then
since it has to be true for all x values, the only possibility is 0 = 0, so
m -8k=0 and 4k-8=0
the latter gives k = 2, then m-8k = 0 gives m=16. </p>
<p>I’m not sure. but that’d be my answer.</p>
<p>I forgot to say the answer was, indeed, 16! You are a freaking math genius. Forgive my ignorance, but how did you get (m-8k)x = 4k-8?</p>
<p>I still don’t get his explanations. Can someone please explain how to solve this problem clearly by steps?</p>
<p>here i’ll try -
x^2 -kx - 8x +8k = x^2 -5kx +m
x^2 cancel so you get: -kx - 8x +8k = -5kx +m => -kx +8x +8k +5kx=m
combine like terms (move 8k to the right hand side) you get: 4kx -8x = m -8k
that’s how you get (4k-8)x=m-8k.</p>
<p>To explain why both 4k-8 and m-8k have to be zero, think about the only possibility for ANY x value to be a solution to this equation, it has to be 0x=0. Otherwise, for some x it’s true, for some it’s not.</p>
<p>Clever. I would have only gotten up to the factored equations. I wouldve never thought of the 0=0 thing. Another thingy in my math bank. :)</p>
<p>shmluza, why is the answer 16 though?</p>
<p>4k-8=0. Solve for k.
m-8k=0. k is known. Solve for m.</p>
<p>^ thx drought.</p>
<p>(x-8)(x-k) = x^2 - 5kx + m</p>
<p>x^2 - kx -8x +8k= x^2 - 5kx + m</p>
<p>anything with 1 x will be part of the middle term, so
-kx -8x will be your middle term for the equation on the left and -5kx will be your middle term on the right. </p>
<p>Since the equations are equal, the middle terms will be equal, so</p>
<p>-kx - 8x = -5kx</p>
<p>everything has 1 x, so you can factor x out to get -k -8 = -5k
solve for k, 4k =8, k=2</p>
<p>8k = m, as these are your end terms in both equations. these will just be constants.</p>
<p>you know k=2,
so 8 * 2 = 16 = m</p>