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Question
By using the method of completing the square, show that the equation `2x^2+x+4=0` has no real roots.
Solution
`2x^2+x+4=0`
⇒`4x^2+2x+8=0` (Multiplying both sides by 2)
⇒`4x^2+2x=-8`
⇒`(2x)^2+2xx2x xx1/2+(1/2)^2=-8+(1/2)^2` [Adding `(1/2)^2`on both sides]
⇒`(2x+1/2)^2=-8+1/4=-31/4<0`
But, `(2x+1/2)^2` cannot be negative for any real value of x.
So, there is no real value of x satisfying the given equation.
Hence, the given equation has no real roots.
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