Answer:
2 or 0 positive zeros
4 or 2 or 0 negative zeros
complex zeros 0,2,4,6
Explanation:
f(x) = x^6 + x^5 + x^4 + 4 x^3 − 12 x^2 + 12
We use Descartes's rule of sign
LEts see the change of sign
f(x) = x^6 + x^5 + x^4 + 4 x^3 − 12 x^2 + 12
In f(x) , there is 2 sign changes
so 2 positive zeros . then subtract 2 to get possible number of zeros
2 or 0 positive zeros
To find negative zeros replace x with -x
f(-x) = (-x)^6 + (-x)^5 + (-x)^4 + 4 (-x)^3 − 12 (-x)^2 + 12
f(x) = x^6 - x^5 + x^4 - 4 x^3 − 12 x^2 + 12
4 sign changes
4 or 2 or 0 negative zeros
complex zeros 0,2,4,6