Video: Finding the Solution Set of Quadratic Equations in R

Find the solution set of the equation 𝑥² + 3 = 0 in ℝ.

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Video Transcript

Find the solution set of the equation 𝑥 squared plus three equals zero in the real numbers.

Let’s begin by finding the solution. So we need to solve for 𝑥. So let’s go ahead and subtract three from both sides of the equation. So we have that 𝑥 squared is equal to negative three.

Now, to solve for 𝑥, we need to square root both sides of the equation. So 𝑥 is equal to the square root of negative three. But we want the solution set of the equation that’s in the real numbers. And the square root of a negative number is not in the real numbers. It’s in the imaginary numbers. So there are no real solutions in this set.

Therefore, the solution set is empty, which is called the empty set or the null set.

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