Question

$2 {x + 3x }^{2} + 4 = 0$

Answer 1

HERE IS YOUR ANSWER

Given :

3x² + 2x + 4 = 0

Dividing both sides by 3, we get

x² + (2/3)x + (4/3) = 0

=> x² + 2.x.(1/3) + (1/3)² - (1/3)² + (4/3) = 0

=> (x + 1/3)² = 1/9 - 4/3

=> (x + 1/3)² = -11/9

=> x + 1/3 = ±(√11)i/3, where i = √(-1)

So,

x + 1/3 = (√11)i/3 and x + 1/3 = -(√11)i/3

=> x = (√11)i/3 - 1/3 and x = -(√11)i/3 - 1/3

=> x = {(√11)i - 1}/3 and x = - {(√11)i + 1}/3

Therefore, the required solution is

x = {(√11)i - 1}/3, - {(√11)i + 1}/3

THANK YOU FOR YOUR QUESTION