The upper part is the question and lower part is my answer.
Is a=-1, b=3, c=1 acceptable?
$\displaystyle \sqrt{1}= \pm 1$ is incorrect. $\displaystyle \sqrt{1}= 1$ since "$\displaystyle \sqrt{a}$" is defined as "the positive x such that $\displaystyle x^2= a$".
It is true that the roots of the equation $\displaystyle x^2= 1$ are 1 and -1, but the reason we say "the roots of equation $\displaystyle x^2= a$ are $\displaystyle x= \pm\sqrt{a}$ is that "$\displaystyle x= \sqrt{a}$" does NOT give both roots.
Hello,
By finding the notation ($\displaystyle \sqrt{a}$) in the text of your question, it is certain that your exercice concern the set of real numbers (not complex numbers) .
The equality $\displaystyle c = \sqrt{a}$ makes sence if and only if the variables a and c are defined as positive real numbers (includes the possible value of zero).
So finding c=-1 makes the value of c out of defined range and thus there is no need to continue calculating the values of a and b.