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^4-9x^2-4x+12#?
According to Rational zeros theorem, in a function such as
zeros are factors of
Here we have
Note that as coefficients of polynomial add up to zero,
Descarte's rule of signs is also method of determining the maximum number of positive and negative real roots of a polynomial.
Under this rule, for positive roots, we start with the sign of the coefficient of the lowest (or highest) power and count the number of sign changes, as you proceed from the lowest to the highest power (or highest to lowest). Here we should ignore powers that are not included i.e. whose coefficients are zeros.
If we have
For negative zeros, we look at
Trial tells us that
Hence, zeros are