4. Determine the number of positive and negative roots of $x^9 - 5x^8 - 14x^7 = 0$
Soln:
Let $P(x) = x^9 - 5x^8 - 14x^7 = 0$
No. of sign changes $= 1$
Max. no. of positive roots $= 1$$P(-x) = -x^9 - 5x^8 + 14x^7 = 0$
No. of sign changes $= 1$
Max. no. of negative roots $= 1$