Just change the variable x with the value x = 2. So, we get:
f(x) = 2x^3 + mx^2 + nx - 3
f(2) = 0 = 2(8) + 4m + 2n - 3
0 = 13 + 4m + 2n. ..(1)
g(x) = 3mx^2 + 2nx + 4
g(2) = 0 = 12m + 4n + 4
0 = 6m + 2n + 2. ..(2)
Using elimination and substitution for both equation (1) and (2), you'll get the values of m and n
Determine the values of a M and N , so that the polynomial 2x^3+mx^2+nx-3 and X^3-3mx^2+2nx+4 are both divisible by x-2.
I am so lost, i do not know how to start this problem! please help i have a test soon!
4 answers
So what is the answer?
Continuing from the partial solution from 10 years ago, except I've fixed the mistake in getting to one of the equations.
(1) -6m + 2n + 6
(2) 4m + 2n + 13
Proceed with elimination:
-6m + 2n + 6 = 4m + 2n + 13
-6m + 6 = 4m + 13
10m = -7
m = -0.7
Proceed with substitution:
(2) 4m + 2n + 13
4(-0.7) + 2n + 13 = 0
-2.8 + 2n + 13 = 0
2n = -10.2
n = -5.1
Hopefully this goes through the solution well enough.
(Also, it's pretty crazy that the first part of this solution was done over 10 years ago... collaboration across time!!!)
(1) -6m + 2n + 6
(2) 4m + 2n + 13
Proceed with elimination:
-6m + 2n + 6 = 4m + 2n + 13
-6m + 6 = 4m + 13
10m = -7
m = -0.7
Proceed with substitution:
(2) 4m + 2n + 13
4(-0.7) + 2n + 13 = 0
-2.8 + 2n + 13 = 0
2n = -10.2
n = -5.1
Hopefully this goes through the solution well enough.
(Also, it's pretty crazy that the first part of this solution was done over 10 years ago... collaboration across time!!!)
How are you getting -6m + 2n + 6 as the one equation? I keep on getting -12m-4n+12. Am I missing a step or just doing it wrong?