Question

By using the method of completing the square, show that the equation `2x^2+x+4=0` has no real roots.  

Answer 1

`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.