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Question
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 – 7x + 3 = 0
Solution
2x2 – 7x + 3 = 0
⇒ 2x2 – 7x = - 3
On dividing both sides of the equation by 2, we get
`⇒ x^2 – (7x)/2 = -3/2`
`⇒ x^2 – 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) = ± 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 1/2
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