Solve each of the following equations:
$$
x^{2}+x+\frac{1}{\sqrt{2}}=0
$$

Answer

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Algebra

NCERT Class 11 - Math

Chapter 5

Complex Numbers and Quadratic Equations

Section 3

Algebra of Complex Numbers

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Video Transcript

All right, Chapter seven, Section seven problem three. We are solving this equation one plus the squared of experts to is equal to zero. Okay, one plus the radical X plus two is equal to zero. We begin by isolating the radical. So we're in a subtract one from all sides. We end up with the square root of X plus to extend not just a little bit is equal to negative one. In order to remove the radical bracket, we need to square both sides. And this quantity squared is just itself. So exploits to equals one and subtract two from both sides and you have X equals negative one. However, if we take that negative one and check, we're going to plug it back in and we're gonna go one plus the square root of negative one plus two equal to zero. And at this point, we are checking. Is this true? Ahh. We have one plus the square root of one. Is it equal to zero? And it's basically saying one plus one equals zero, which is not true. And so there is no real solution here. Often called the no set

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