Question

1. Find the roots of the following quadratic equations, if they exist, by the method of
completing the square:
(1) 2x2 - 7x +3=0
(ii) 2x2 + x-4=0
(1) 4x + 4/3x + 3 = 0
(iv) 2x2 + x +4=0
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Answer 1

Answer:

1. answer..!! solution

Answer 2

(i) 2x2 – 7x + 3 = 0 ⇒ 2x2 – 7x = – 3

Dividing by 2 on both sides, we get

⇒ x2 -7x/2 = -3/2

⇒ x2 -2 × x ×7/4 = -3/2

On adding (7/4)2 to both sides of equation, we get

⇒ (x)2-2×x×7/4 +(7/4)2 = (7/4)2-3/2

⇒ (x-7/4)2 = (49/16) – (3/2)

⇒(x-7/4)2 = 25/16  

⇒(x-7/4)2 = ±5/4

⇒ x = 7/4 ± 5/4

⇒ x = 7/4 + 5/4 or x = 7/4 – 5/4

⇒ x = 12/4 or x = 2/4

⇒ x = 3 or x = 1/2

(ii) 2x2 + x – 4 = 0 ⇒ 2x2 + x = 4

Dividing both sides of the equation by 2, we get

⇒ x2 +x/2 = 2

Now on adding (1/4)2 to both sides of the equation, we get,  

⇒ (x)2 + 2 × x × 1/4 + (1/4)2 = 2 + (1/4)2

⇒ (x + 1/4)2 = 33/16

⇒ x + 1/4 = ± √33/4

⇒ x = ± √33/4 – 1/4

⇒ x = ± √33-1/4

Therefore, either x = √33-1/4 or x = -√33-1/4