If x 2 and x−1 are factors of
the expression lx3
+ 2kx2
+ 24
=0, find the value of l and k
If x^2 and x-1 are factors of the expression, then we can write the expression as:
lx^3 + 2kx^2 + 24 = (x^2)(x-1)
Expanding the right side:
lx^3 + 2kx^2 + 24 = x^3 - x^2
Now we can equate the corresponding terms:
lx^3 = x^3
2kx^2 = -x^2
24 = 0 (since there are no constant terms on the right side)
From the first equation, we can determine that l = 1.
For the second equation, we have:
2kx^2 = -x^2
Divide both sides by x^2:
2k = -1
Solving for k:
k = -1/2
So, the values of l and k are 1 and -1/2, respectively.
To find the value of l and k, we can start by using the given information about the factors:
We know that x^2 and x-1 are factors of the expression.
If x^2 is a factor, then the expression can be written as:
l(x^2) + 2kx^2 + 24 = 0
Simplifying, we get:
(x^2)(l + 2k) + 24 = 0 ----(1)
Now, if x - 1 is a factor, then the expression can also be written as:
l(x - 1) + 2k(x - 1) + 24 = 0
Simplifying, we get:
(l + 2k)(x - 1) + 24 = 0 ----(2)
Comparing the equations (1) and (2), we can equate the coefficients of (x^2) and (x - 1):
l + 2k = 0 ----(3)
Now, to find the value of l and k, we need additional information or equations. Without any other information, we cannot determine the specific values of l and k.