1.

Solve the quadratic equations by factorization method only:4x2 + 1 = 0

Answer»

Given as 4x2 + 1 = 0

As we know, i2 = –1 ⇒ 1 = –i2

On substituting 1 = –i2 in the above equation, we get

4x2 – i2 = 0

(2x)2 – i2 = 0

[On using the formula, a2 – b2 = (a + b) (a – b)]

(2x + i) (2x – i) = 0

2x + i = 0 or 2x – i = 0

2x = –i or 2x = i

x = -i/2 or x = i/2

∴ The roots of the given equation are i/2, -i/2



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