Descartes Rule

[ronaldo_rm]

I need to show that x^3 + a^2 x + b^2 = 0 has one negative and two imaginary roots if b does not equal 0. I know how to show one negative root but I don't know how to show the imaginary roots.

 

[tkhunny]

What is Descartes' Rule of Signs?

You may wish to note:
a^2 > 0
b^2 > 0

 

[stapel]

What is Descartes' Rule of Signs?

Descartes' Rule is a way of determining the maximum number of positive and negative roots of a polynomial.

Eliz.

 

[tkhunny]

You gave it away. Surely it's in the book.

 

[stapel]

You gave it away.

Sorry.

They don't always cover this Rule nowadays, since the kiddos are expected to do everything off the graphing calculator....

Eliz.

 

[tkhunny]

No worries.

In any case, the important point is that the constants are positive. Only then can we evaluate the "Rule".