AKumar
Answered

Find the best solutions to your questions at Westonci.ca, the premier Q&A platform with a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a community of experienced experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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.

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.