no. of real roots

[stuart clark]

number of real roots of the equation x⁸-x⁵+x²-x-1=0

[Lokman Gökçe]

Let f(x) = x⁸ - x⁵, g(x) = -x² + x + 1.

We write that f(x) = x⁵(x³ - 1).  x = 0 is a five multiple root and x = 1 is a simple root. Also x = 0 is turning point of f. If we draw graph of y = f(x) curve and y = g(x) parabola, we see that thare are two intersection points of f(x) = g(x)

[stuart clark]

Thanks Admin