Find integers that are upper and lower bounds for the real zeros of the polynomial. P(x) = x^4 − 2x^3 + x^2 − 9x + 2

Answer 1

p = {+-1, +-2}

q = {+-1}

p/q = {+-1,+-2}

None of them work, so there are no rational solutions.

The solutions must be found numerically, perhaps by examining the graph.

One solution is x=0.226 the other is x=2.738

the other two solutions are complex/imaginary.

the lower bound is zero and the upper bound is 3.

So a numerical algorithm can use the interval [0,3] as starting approximation.