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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 + 1/(2x) = 2`
`⇒ x^2 + 2 × x × 1/4 = -2`
On adding (1/4)2 to both sides of the equation, we get
`⇒ (x)^2 + 2 × x × 1/4 + (1/4)^2 = (1/4)^2 - 2 `
`⇒ (x + 1/4)^2 = 1/16 - 2`
`⇒ (x + 1/4)^2 = -31/16`
However, the square of number cannot be negative.
Therefore, there is no real root for the given equation
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