Solve each of the following equations:  x² + x/√2 + 1 = 0

Solution:

The given quadratic equation is x² + x/√2 + 1 = 0

This equation can also be written as √2x² + x + √2 = 0

On comparing the given equation with ax² + bx + c = 0,

We obtain a = √2, b = 1, and c = √2

Therefore, the discriminant of the given equation is

D = b² - 4ac

= (- 1)² - 4 x √2 x √2

= 1 - 8

= - 7

Hence, the required solutions are

(- b ± √D)/2a = (- (1) ± √- 7/(2 x √2)

= [- 1 ± i(√ 7)] / (2√2) [∵ √- 1 = i]

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NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.3 Question 10

Solve each of the following equations:  x² + x/√2 + 1 = 0

Summary:

A complex equation x² + x/√2 + 1 = 0 is given. We have found that the solutions of the equation are [- 1 ± i(√ 7)] / (2√2)