Given X & sup3; - 16x & sup2; + mx-n divided by X & sup2; - 2x + 3, the remainder is - 18x + 15. Try to find the value of M, n

Given X & sup3; - 16x & sup2; + mx-n divided by X & sup2; - 2x + 3, the remainder is - 18x + 15. Try to find the value of M, n


(X³-16X²+mx-n)÷(x²-2x+3)=(x-14).(m-31)x+(42-n)
So m-31 = - 18,42-n = 15, so m = 13, n = 27



When using MATLAB to solve the equation, if the range of unknowns is limited, such as X * sin (x) - 1 / 2 = 0, the solution of the equation from - 10 to 10 is solved?
>> x=solve('sin(x)*cos(x)-x*x=0')
x =
matrix([[0]])
This equation has only two solutions. Why is the answer like this?


f=@(x)x.*sin(x)-1/2;x=fsolve(f,[-10:1:10])x =Columns 1 through 6-9.3714 -9.3714 -6.3619 -6.3619 -2.9726 -2.9726Columns 7 through 12-0.7408 0.7408 2.9726 2.9726 2.9726 6.3619Columns 13 through 156.3619...



Solution of MATLAB equations when the number of equations is greater than the number of unknowns
syms xn yn zn xt yt zt
[o3,o4,o5,o6]=solve('cos(o3)*cos(o4)*cos(o5)-sin(o3)*sin(o5)=xn','cos(o3)*cos(o4)*cos(o5)+cos(o3)*sin(o5)=yn','-sin(o4)*cos(o5)=zn','(-cos(o3)*cos(o4)*sin(o5)-sin(o3)*cos(o5))*cos(o6)+cos(o3)*sin(o4)*sin(o6)=xt','(-sin(o3)*cos(o4)*sin(o5)+cos(o3)*cos(o5))*cos(o6)+sin(o3)*sin(o4)*sin(o6)=yt','sin(o4)*sin(o5)*cos(o6)+cos(o4)*sin(o6)=zt','o3,o4,o5, o6')
The old way is warm-hearted. If you are passing by, you can give me your advice!
I simplified the original six equations, reduced two, and input them into Matlab, but they still can't be solved. The simplified equations are as follows:
syms xn yn zn xt yt zt
[o3,o4,o5,o6]=solve('xn*cos(o3)+yn*sin(o3)=cos(o4)*cos(o5)','-sin(o4)*cos(o5)=zn','xt*cos(o3)+yt*sin(o3)=sin(o4)*sin(o6)-cos(o4)*sin(o5)*cos(o6)','sin(o4)*sin(o5)*cos(o6)+cos(o4)*sin(o6)=zt','o3,o4,o5,o6')


The equation whose number of equations is greater than the number of unknowns is called overdetermined equation in my impression. You can refer to advanced algebra or calculation method, and I forgot how to solve it. However, it seems that the method of matrix can be used. These contents are only learned by mathematics majors. They have never seen anything about engineering mathematics, so they will be surprised like upstairs~



Is it true that only a and B represent the coefficients and constants of the unknowns in the linear equation of one variable?


No. for example
kx+c =0