show that the polynomial p (x)=2x^4 - 7x^3-10x^2+21x-12 has a zero that lies between x=0 and x=2

Question

I tried with the intermediate value but it doesn't work

Answer 1

The expectation is not true, at least according to putting the function into a graphing tool.

There is a local maximum between x=0 and x=2, but the graph does not touch the x-axis.

May be a complex zero with imaginary part?

You would expect the polynomial to have four complex zeros.

Source:  http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions.faq.question.868375.html