Question -
Answer -
Given: x2 +2x + 2 = 0
x2 +2x + 1 + 1 = 0
x2 +2(x)(1) + 12 + 1 = 0
(x + 1)2 +1 = 0 [∵ (a + b)2 =a2 + 2ab + b2]
We know, i2 =–1 ⇒ 1 = –i2
By substituting 1 = –i2 inthe above equation, we get
(x + 1)2 +(–i2) = 0
(x + 1)2 –i2 = 0
(x + 1)2 –(i)2 = 0
[Byusing the formula, a2 – b2 = (a + b) (a – b)]
(x + 1 + i) (x + 1 –i) = 0
x + 1 + i = 0 or x + 1– i = 0
x = –1 – i or x = –1 +i
x = -1 ± i
∴ The roots of thegiven equation are -1 ± i