I took my calculus test and wondering if I got this answer wrong or at least partially correct?

the problem looked like 5x^5/2 + 2x^3/2 - 7x^1/2

so I factored out x^1/2 and then I solved the other part using the quadratic formula. the problem is i got 3 solutions to x = 0, -1, and then a fraction. the exact numbers arent like they were on the test just a similar form. problem is on my graphing calculator it only showed 0, -1 as x solutions so i put that as my answer excluding the fraction. is that technically right? or should the fraction have been included as well?

I only included the the solutions that crossed the x axis on the graph?