How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=x^3-2x^2-5x+6#?
1 Answer
See explanation...
Explanation:
Given:
#f(x) = x^3-2x^2-5x+6#
By the Rational Zeros theorem, any rational zeros of
That means that the only possible rational zeros are:
#+-1, +-2, +-3, +-6#
The pattern of signs of the coefficients of
The pattern of signs of the coefficients of
In addition, note that the sum of the coefficients of
#1-2-5+6 = 0#
Hence we can tell that
#x^3-2x^2-5x+6 = (x-1)(x^2-x-6) = (x-1)(x-3)(x+2)#
So the other two zeros of