MathDB

Suppose that

a

and

b

are real numbers such that the quadratic polynomial f(x)\equal{}x^2\plus{}ax\plus{}b has no nonnegative real roots. Prove that there exist two polynomials

g,h

whose coefficients are nonnegative real numbers such that: f(x)\equal{}\frac{g(x)}{h(x)} for all real numbers

x

Problem Statement