Let P(x)=0 be eqn w/ non-zero real root. State sufficient condition on coeff. s.t....

[popcorn123]

Let P(x) = 0 be an equation whose roots are all non zero real numbers. State a sufficient condition on the coefficients of p(x) that will ensure that the roots of P(x) = 0 occur in reciprocal pairs. That is, if k is a root of p(x) where k doesn't equal 0 and is a real number, then -/k must also be a root. Prove this for fifth and sixth degree polynomials.

 

[stapel]

Let P(x) = 0 be an equation whose roots are all non zero real numbers. State a sufficient condition on the coefficients of p(x) that will ensure that the roots of P(x) = 0 occur in reciprocal pairs. That is, if k is a root of p(x) where k doesn't equal 0 and is a real number, then -/k must also be a root. Prove this for fifth and sixth degree polynomials.

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

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