How to solve quadratic equation which includes a vector?

Hi,

I have the following equation: V1^2 - V1*V2 - Q*Z = 0

V1 is what I need to find

V2 is a known constant

Q is a known vector with complex values

Z is a known constant

This is what I've tried:

syms V1
eq = V1^2 - V1*V2 - Q*Z;
result = roots(eq);

But I get the result "Empty sym: 0-by-1"

Answer 1

[Bastian Arturo Romero Mardones]

You can try with solve:

syms V1
eq = V1^2 - V1*V2 - Q*Z;
result = solve(eq,V1);

[Lu Da Silva]

I tried and get a result that states: val = x.

Is there a way to solve it with a for-loop perhaps?

[Bastian Arturo Romero Mardones]

You can try with eval():

syms V1
eq = V1^2 - V1*V2 - Q*Z;
result = solve(eq,V1);
result = eval(result)

or roots()

V2 = 1; Q = 2; Z = 3; %Values of example
eq2 = [1 -V2 -Q*Z]; %Equivalent to V1^2-V1*V2-Q*Z
result2 = roots(eq2);

to this case don't need for loop

[Lu Da Silva]

when using eval() i get a 0x0 double (no result)

whereas when trying to use roots() I get the error: "Dimensions of arrays being concatenated are not consistent"

I think I need to try a for loop like:

for i = 1:length(Q)
    syms x
    eqn = x^2 - V2*x - Q*Z;
    solx = solve(eqn, x);
end

But it doesn't work either, as I get: "Empty sym: 0-by-1"

[Bastian Arturo Romero Mardones]

Now understand, i don't considered Q with a vector. In this case you need to use a loop.

Q = [1+3i 2+2i 3+4i 4+2i]; %Example
V2 = 1; Z = 8; 
for  i = 1:length(Q)
    eq2 = [1 -V2 -Q(i)*Z];
    result2 = roots(eq2)
    result{i} = result2;
end

sorry :D

In this case you should only change Q by Q (i)

for i = 1:length(Q)
    syms x
    eqn = x^2 - V2*x - Q(i)*Z; %% Change Q ---> Q(i);
    solx = solve(eqn, x);
end

[Lu Da Silva]

The former loop worked, yet I only get one result: the positive and negative result of the last value of my Q-vector... Shouldn't I get a vector/matrix as a result? Maybe roots isn't the right function for this case...? For some reason it's not saving all the values yet just the last one

[Lu Da Silva]

Figured it out; it's

for i = 1:length(Q)
    eq2 = [1 -V2 -Q(i)*Z];
    result(i,:) = roots(eq2)
end

Thank you!