So y = 0 when x is in between -1 and 0. for x >0 , y >0 and increasing. For x < -1 , y is decreasing more and more. So there is only one real root -1 < α < 0.
Slope of y : 1+3x^2+5x^4+7x^6+9x^8. it is always positive. So y is always increasing as x increases. So y = 0 is possible only once.
You can find that approximately as: - 0.63