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Question
Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x2 + x – 4 = 0
Solution
2x2 + x – 4 = 0
⇒ 2x2 + x = 4
On dividing both sides of the equation, we get
`⇒ x^2 + x/2 = 2`
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 = ± sqrt33/4`
`⇒ x = ± sqrt33/4 - 1/4`
`⇒ x = ± sqrt33-1/4`
`⇒ x = (sqrt33-1)/4 `
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