Question

Find and upper bound and a lower bound for the zeros of the following polynomial function.
h(x)=x^4+2x^3-11x^2-14x+24

Answer 1

Assuming the question is on the number of positive, negative or complex zeros, you can use the Descartes' rule of signs - https://en.wikipedia.org/wiki/Descartes%27_rule_of_signs

Then you'll find that the function has 0 or 2 positive roots or 0 or 2 negative roots. The number of complex roots then is 4 - (2 + 2) = 0 based on the Wikipedia article.

Because this is a 4th-order polynomial, there will always be 4 zeros. The minimum real zeros that this particular one could have based on sign changes is 0 and the max is 4.

In reality, this function has 2 positive roots and 2 negative \(\href{http:///www.wolframalpha.com/input/?i=zeros+of+x%5E4%2B2x%5E3-11x%5E2-14x%2B24}{roots} \).

Hope this helps :-)