Solve the following quadratics
x2 – 4x + 7 = 0
Given x2 – 4x + 7 = 0
⇒ x2 – 4x + 4 + 3 = 0
⇒ x2 – 2(x)(2) + 22 + 3 = 0
⇒ (x – 2)2 + 3 = 0 [∵ (a – b)2 = a2 – 2ab + b2]
⇒ (x – 2)2 + 3 × 1 = 0
We have i2 = –1 ⇒ 1 = –i2
By substituting 1 = –i2 in the above equation, we get
(x – 2)2 + 3(–i2) = 0
⇒ (x – 2)2 – 3i2 = 0
Since a2 – b2 = (a + b)(a – b), we get
Thus, the roots of the given equation are.