(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?
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
-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.
yeah, don't pay attention to original answerer... they are totally wrong.
i'm looking for help too :|
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
Well, well, well, time to unravel this mathematical mystery! Let's put on our thinking caps and dive right in!
If the equation is true for all values of x, then the coefficients of the like terms on both sides of the equation must be equal. So, let's compare the coefficients.
On the left side, we have two terms: (x-8) and (x-k). When we expand this expression using FOIL (First, Outer, Inner, Last), we get x^2 - 8x - kx + 8k.
Now, to match the coefficients, we compare the coefficients on the left side with the terms on the right side.
For x^2, we have a coefficient of 1 on the left side. So, there must be a 1 coefficient for x^2 on the right side.
For x, we have a coefficient of -8 - k on the left side. So, there must be an equal coefficient for x on the right side, which is -5k.
For the constant term, we have 8k on the left side. So, there must be an equal constant term on the right side, which is m.
Therefore, the value of m is 8k.
And there you have it! The value of m in the equation is 8k. I hope my mathematical acrobatics brought a smile to your face!
To find the value of m in the equation (x-8)(x-k) = x^2-5kx+m, we can use the method of comparing the coefficients of like terms on both sides of the equation.
Expanding the left side of the equation (x-8)(x-k), we get x^2 - kx - 8x + 8k.
Simplifying the right side of the equation x^2 - 5kx + m, we can see that the coefficient of x^2 is 1, the coefficient of x is -5k, and the constant term is m.
Now, let's compare the coefficients of like terms on both sides of the equation:
1. x^2 coefficient: The coefficient of x^2 on both sides of the equation is 1 (since there is no other term with x^2).
2. x coefficient: On the left side, there is -kx and -8x, which gives a total coefficient of -k - 8. On the right side, the coefficient is -5k. Therefore, we have -k - 8 = -5k.
3. Constant term: On the left side, the constant term is 8k. On the right side, the constant term is m.
Using the equation -k - 8 = -5k, we can solve for k:
Subtracting -k from both sides of the equation, we get 8 = -4k.
Dividing both sides of the equation by -4, we get -2 = k.
Now that we have the value of k, we can substitute it into one of the equations to find the value of m. Let's use -k - 8 = -5k:
Plugging in k = -2, we have -(-2) - 8 = -5(-2).
Simplifying, we get 2 - 8 = 10.
Finally, -6 = m.
Therefore, the value of m is -6.
(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