AKumar
Answered

Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Connect with a community of experts ready to help you find accurate solutions to your questions quickly and efficiently. Our platform provides a seamless experience for finding reliable answers from a network of experienced 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 using our platform. We're always here to provide accurate and up-to-date answers to all your queries. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.