A level pure maths question

The question gave me a cubic equation and told me to prove it has no stationary points. I differentiated it which gave me a quadratic and I equated it to 0 and tried to use the quadratic formula to solve it. The square root part of the equation gave me a negative number which I said proved there is no stationary points. However the mark scheme said to use the discriminant, would my method get the marks?

The part of the quadratic formula inside the square root bracket is the discriminant. I would have thought your method should get the marks. However, it is a bit more than strictly required as it is sufficient simply to show that b^2-4ac < 0 (combined with a short verbal conclusion).