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