Q. 24.3( 6 Votes )
Solve the following quadratic equations by factorization method
9x2 + 4 = 0
Answer :
Given 9x2 + 4 = 0
⇒ 9x2 + 4 × 1 = 0
We have i2 = –1 ⇒ 1 = –i2
By substituting 1 = –i2 in the above equation, we get
9x2 + 4(–i2) = 0
⇒ 9x2 – 4i2 = 0
⇒ (3x)2 – (2i)2 = 0
⇒ (3x + 2i)(3x – 2i) = 0 [∵ a2 – b2 = (a + b)(a – b)]
⇒ 3x + 2i = 0 or 3x – 2i = 0
⇒ 3x = –2i or 3x = 2i
Thus, the roots of the given equation are
.
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