AKumar
Answered

At Westonci.ca, we provide reliable answers to your questions from a community of experts. Start exploring today! Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.

Let p(x) be a polynomial with real coefficients such that the product of all six roots of p(x) is negative. Show that if the degree of p(x) is 6, then p(x) has at least one positive root.

Sagot :

mhanifa

Answer:

The product of 6 numbers is negative only is the number of negatives is odd.

If the number of negative roots is even, then their product will be positive.

The greatest odd number less than 6, is 5. It means the smallest number of positive numbers is 6 - 5 = 1.

So the least number of positive roots is one.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.