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how many real - number solutions does the equation (x^{2}+12 = 0) have?…

Question

how many real - number solutions does the equation (x^{2}+12 = 0) have?
options: 2, 3, 4, none

Explanation:

Step1: Rearrange the equation

$x^2 = -12$

Step2: Analyze real number properties

For all real $x$, $x^2 \geq 0$

Step3: Compare with result

$-12 < 0$, so no real $x$ satisfies $x^2=-12$

Answer:

none