Solve the quadratic equations by factorization method only x2 – 4x + 7 = 0

Asked by Sakshi | 1 year ago |  55

##### Solution :-

Given: x2 – 4x + 7 = 0

x2 – 4x + 4 + 3 = 0

x2 – 2(x) (2) + 22 + 3 = 0

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

(x – 2)2 + 3 × 1 = 0

We know, i2 = –1 ⇒ 1 = –i2

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

(x – 2)2 + 3(–i2) = 0

(x – 2)2 – 3i2 = 0

(x – 2)2 – $$(\sqrt{3i})^2$$ = 0

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

$$(x – 2 + \sqrt{3i}) (x – 2 – \sqrt{3i}) = 0$$

$$x = 2 ± \sqrt{3i}$$

The roots of the given equation are $$x = 2 ± \sqrt{3i}$$

Answered by Aaryan | 1 year ago

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