Solve each of the equation in Exercises 6 to 9: 27x² - 10x + 1 = 0

Solution:

The given quadratic equation is,

27x² – 10x + 1 = 0

By comparing this with ax² + bx + c = 0, we get a = 27, b = -10, and c = 1.

Its discriminant is, D = b² - 4ac = (-10)² - 4(27)(1) = -8

The solutions of the given quadratic equation are,

(- b ± √D)/2a = (10 ± √(-8) ) / 2(27)

= (10 ± i√8) / 54 [∵ √- 1 = i]

= (10 ± 2i√2) / 54

= 5/27 ± (54/√2) i

= 5/27 ± (√2 /27) i  [∵ 1/√2 = 1/√2 ·√2/√2 = √2/2)

Hence the solutions of the quadratic equation 27x² – 10x + 1 = 0 are x = x = 5 / 27 + i√ 2 / 27, 5 / 27 - i√ 2 / 27

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 8

Solve each of the equation in Exercises 6 to 9: 27x²- 10x + 1 = 0

Summary:

The solutions of the quadratic equation 27x² - 10x + 1 = 0 are x = x = 5 / 27 + i√ 2 / 27, 5 / 27 - i√ 2 / 27