What are the values of a and b that make 1 into a root of P with multiplicty 2
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > What are the values of a and b that make 1 into a root of P with multiplicty 2

What are the values of a and b that make 1 into a root of P with multiplicty 2

[From: ] [author: ] [Date: 11-04-22] [Hit: ]
For 1 to be a root, P(1) = 0.For it to be a root of multiplicity 2, it must have a max/min at 1, so P(1)=0.P(1)=1-2-5+a-3+b-3 = 0,......
Find the values of a and b so that 1 is a root of multiplicty 2 of the polynomial

P(x) = x^873 - 2x^401 - 5x^14 + ax^5 - 3x³ + bx -3

This seems a very messy problem. Is there any easy way to solve this?

Thank you.

-
Yes. For 1 to be a root, P(1) = 0. For it to be a root of multiplicity 2, it must have a max/min at 1, so P'(1)=0.

P(1)=1-2-5+a-3+b-3 = 0, so a+b =12

P'(1) = 873 - 802 - 70 + 5a - 6 + b = 0 so 5a + b = 5

this yields a = -7/4, b = 55/4

I did the work in my head, so double check that, but the principle is sound.
1
keywords: and,root,of,that,are,multiplicty,into,make,values,with,What,the,What are the values of a and b that make 1 into a root of P with multiplicty 2
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .