Use Descartess rule of signs to state the number of possible

Use Descartes\'s rule of signs to state the number of possible positive and negative real roots. (Enter your answers as a comma-separated list.) x^4 + 2x^3 -17x^2 - 5x + 15 = 0 number of possible positive real roots______number of possible negative real roots_______

Solution

f(x) = x^4 +2x^3 - 17x^2 - 5x +15

Using Descarte\'s Rule :

There are two sign changes , so number of +ve real roots = 0, 2

Now f(-x) = x^4 - 2x^3 - 17x^2 + 5x +15

There are two sign changes , so number of -ve real roots = 0, 2