By using the method of completing the square, show that the equation 2x2 + x + 4 = 0 has no real roots.
2x2 + x + 4 = 0
4x2 + 2x + 8 = 0 (multiplying both sides by 2)
4x2 + 2x = - 8
[Adding on both sides]
using a2 + 2ab + b2 = (a + b)2
But 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.