Find conditions such that symbolic expression is real-valued

I have a set of symbolic expressions of several variables, and I want Matlab to find the conditions on the variables such that the expressions meet certain criteria, such as being real-valued or one expression being less than another. For example,

syms a b c x;
x = solve(a*x^2 + b*x + c == 0,x)

returns the familiar quadratic formula as a vector:

x =

   -(b + (b^2 - 4*a*c)^(1/2))/(2*a)
   -(b - (b^2 - 4*a*c)^(1/2))/(2*a)

For these two solutions for x, I'd like to know: (a) the conditions on a, b, and c such that x is real-valued (obviously b^2 > 4*a*c for this example); (b) the conditions on a, b, and c such that x(1) > x(2).

If it helps, I know that all my symbolic variables (a, b, and c in the example) are positive-valued. Also, I'm only interested in positive values of x.

Thanks, Rich

[Walter Roberson]

For the quadratic, x(2) >= x(1) provided that both are real-valued. (If they have imaginary components then comparing them is not well defined.)

Answer 1

[Stefan Wehmeier]

a)

feval(symengine, 'solve', a*x^2 + b*x + c, x, 'Real', 'IgnoreSpecialCases')

You may omit the IgnoreSpecialCases, which shows you that a<>0 must also be satisfied (obviously).

b) It is better to solve for only one variable:

 feval(symengine, 'solve', x(1) > x(2), a, 'Real')

You haven't declared your syms to be real, but the real mode in the solver treats them as reals which I think is what you want.