# Two Quadratics are equal find K1 and K2 cancel out X

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Madyson Davis on 4 Mar 2023
Edited: VBBV on 5 Mar 2023
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 = 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?

VBBV on 5 Mar 2023
Edited: VBBV on 5 Mar 2023
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 = 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