Solve each of the following equations: x² + 3x + 9 = 0

Solution:

The given quadratic equation is x² + 3x + 9 = 0

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

We obtain a = 1, b = 3, and c = 9

Therefore, the discriminant of the given equation is

D = b² - 4ac

= 3² - 4 x 1 x 9

= - 27

Therefore, the required solutions are

(- b ± √D)/2a = (- 3 ± √- 27)/(2 x 1)

= (- 3 ± 3√- 3)/2

= (- 3 ± 3i√3)/2 [∵ √- 1 = i]

NCERT Solutions Class 11 Maths Chapter 5 Exercise 5.3 Question 3

Solve each of the following equations: x² + 3x + 9 = 0

Summary:

A complex equation x² + 3x + 9 = 0 is given. We have found that the solutions of the equation are (- 3 ± 3i√3)/2