we first used newtons method to find the approximate value of 200^(1/7) and got it equal to the awnser in the caclulator which is = 2.131663117

i need some help in the right direction on how to solve the question after solving the above equation using newtons method!

Question:

the fundamental theorem of algebra guarantees that the equation x^7-200 = 0 must have 7 solutions. You have just found one of these. Are there any more real solutions? Use your tools of calculus to sustain your awnser.