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

Question

Philoid · Accepted Answer

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.