Two Quadratics are equal find K1 and K2 cancel out X

So I am coding something that will include two variables that are taking place of constants in a quadratic equation. We have a quadratic that is equal to the first equation so we can solve it by hand but I want to verify my numbers. However the solutions for K1 and K2 keep getting messed up by the x value (which in this code is deemed l) which should cancel out.

A =[1 -1; 0 0];
B = [0; 1];
MC = ctrb(A,B); %Gives controllability matrix
det (MC) %Not zero so is controllable 

ans = 1

syms K1 K2 l
Atil = A-B*[K1 K2]

Atil = 

lambda = [l 0;0 l] ;
opt1 = det(lambda-Atil) % quadratic with K1 and K2 values

opt1 = 

opt2 = l^2+1.5*l+0.5 %set quadratic

opt2 = 

solve (opt1==opt2,K1,K2)

ans = struct with fields:
    K1: - (5*l)/2 - 1/2
    K2: 0

as you can see both can be put into the form of l^2+number*l+number so you should be able to take each section before the l to set it equal but I am not sure how to set that up correclty in matlab without individually manually making each section a variable anyone know an automated way for it?

Answer 1

[VBBV]

A =[1 -1; 0 0];
B = [0; 1];
MC = ctrb(A,B); %Gives controllability matrix
det (MC) %Not zero so is controllable 

ans = 1

syms K1 K2 l
Atil = A-B*[K1 K2]

Atil = 

lambda = [l 0;0 l] ;
opt1 = det(lambda-Atil)  % quadratic with K1 and K2 values

opt1 = 

opt1 = collect(opt1)   % you can now equate the like terms of opt1 and opt2 and solve for K1 and K2

opt1 = 

opt2 = l^2+1.5*l+0.5  %set quadratic

opt2 = 

Sol = solve (opt1==opt2,[l,K1,K2])

Sol = struct with fields:
     l: [2×1 sym]
    K1: [2×1 sym]
    K2: [2×1 sym]

Sol.l

ans = 

Sol.K1

ans = 

Sol.K2

ans = 

sol = solve(opt1 == opt2,l)

sol = 

Use collect to rearrange the equation