Solve the quadratic equations by factorization method only 4x2 – 12x + 25 = 0

Asked by Sakshi | 1 year ago |  71

##### Solution :-

Given: 4x2 – 12x + 25 = 0

4x2 – 12x + 9 + 16 = 0

(2x)2 – 2(2x)(3) + 32 + 16 = 0

(2x – 3)2 + 16 = 0 [Since, (a + b)2 = a2 + 2ab + b2]

(2x – 3)2 + 16 × 1 = 0

We know, i2 = –1 ⇒ 1 = –i2

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

(2x – 3)2 + 16(–i2) = 0

(2x – 3)2 – 16i2 = 0

(2x – 3)2 – (4i)2 = 0

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

(2x – 3 + 4i) (2x – 3 – 4i) = 0

2x – 3 + 4i = 0 or 2x – 3 – 4i = 0

2x = 3 – 4i or 2x = 3 + 4i

x = $$\dfrac{3}{2}$$ – 2i or x = $$\dfrac{3}{2}$$ + 2i

The roots of the given equation are $$\dfrac{3}{2}$$ + 2i, $$\dfrac{3}{2}$$ – 2i

Answered by Aaryan | 1 year ago

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