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There are two quadratic polynomials as follow

$$Ax^2 + Bx + C = 0$$

and

$$Ax^2 + Bx - C = 0$$

is it true to claim that at least one of the equations has at least one positive complex or real solution?

if $\dfrac{C}{A} > 0, -\dfrac{B}{A} < 0$ and $\Delta = B^2-4AC > 0$ then there are two positive real solutions and if $\dfrac{C}{A} < 0, \Delta > 0$ there is a one positive and one negative solution. But I have no idea about the complex roots and whether at least one of the polynomials has at least one positive complex or real root.

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2 Answers

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You are correct about the real roots. In case of complex roots we do not have an order system for complex numbers. If you have complex roots and your coefficients are real numbers, then complex roots appear in cojugate pairs and the real parts are positive or negative depending on the sign of $-B/A$

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It's wrong for $C=0$. Take $$x^2+x=0.$$

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