Question

b. ( x^2 = -12 )

Explanation:

Step1: Recall square root of negative numbers

For the equation \(x^{2}=- 12\), we know that in the real number system, the square of a real number is non - negative. So we need to use the concept of imaginary numbers. The imaginary unit \(i=\sqrt{-1}\).

Step2: Solve for x

Take the square root of both sides of the equation \(x^{2}=-12\). We get \(x = \pm\sqrt{-12}\). Then we can rewrite \(\sqrt{-12}\) as \(\sqrt{12}\times\sqrt{-1}\). Since \(\sqrt{12} = 2\sqrt{3}\) and \(\sqrt{-1}=i\), we have \(x=\pm2\sqrt{3}i\).

Answer:

\(x = \pm2\sqrt{3}i\)