# polynomials – How can I solve this PreRMO 2019 problem 23?

Let $$t$$ be the area of a regular pentagon with each side equal to $$1$$. Let $$P(x)=0$$ be the polynomial equation with least degree, having integer coefficients, satisfied by $$x=t$$ and the $$gcd$$ of all the coefficients equal to $$1$$. If $$M$$ is the sum of the absolute values of the coefficients of $$P(x)$$, What is the integer closest to $$sqrt{M}$$ ? ($$sin 18^{circ}=(sqrt{5}-1)/2$$)

Here in this problem I first started out by trying to find out the area of the pentagon, but that dosn’t really help. Also some people claimed that the value of $$sin 18 neq (sqrt{5}-1)/2$$ but instead it is $$(sqrt{5}-1/4)$$. That is another thing that bothers me, but I wanted to know about what is the motivation behind your solution.