Solve the following quadratic equations by factorization method
x2 + 1 = 0
Given x2 + 1 = 0
We have i2 = –1 ⇒ 1 = –i2
By substituting 1 = –i2 in the above equation, we get
x2 – i2 = 0
⇒ (x + i)(x – i) = 0 [∵ a2 – b2 = (a + b)(a – b)]
⇒ x + i = 0 or x – i = 0
⇒ x = –i or x = i
∴ x = ±i
Thus, the roots of the given equation are ±i.