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in Quadratic Equations by (29.7k points)
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Solve the following quadratics 

4x2 + 1 = 0

1 Answer

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Best answer

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 

⇒ x = \(-\frac{1}{2}i \ or \frac{1}{2}i\)

∴ x = ± \(\frac{1}{2}\) i

Thus, the roots of the given equation are  ± \(\frac{1}{2}\) i

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