Welcome :: Homework Help and Answers :: Mathskey.com

Recent Visits

    
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,849 users

Find the roots of the polynomial equation -x^3 + 5x^2 - 11x + 55 = 0.

0 votes

Find the roots of the polynomial equation -x^3 + 5x^2 - 11x + 55 = 0.

asked Feb 24, 2014 in ALGEBRA 2 by rockstar Apprentice

2 Answers

0 votes

Given polynomial equation -x^3+5x^2-11x+55 = 0

By synthatic division

image

image

image

image

image

image

image

image

 

answered Feb 25, 2014 by david Expert
0 votes

 

Identify Rational Zeros  

Usually it is not practical to test all possible zeros of a polynomial function using only synthetic substitution. The Rational Zero Theorem can be used for finding the some possible zeros to test.

- x3+ 5x2- 11x + 55 = 0

If p/q is a rational zero, then is a factor of 55 and is a factor of 1.

The possible values of p  are   ± 1,   ± 5, ± 11 and  ± 55,.

The possible values for q are ± 1.

So, p/q = ± 1,   ± 5, ± 11,± 55.

Make a table for the synthetic division and test possible  zeros.

p/q -1 5 -11 55
1 -1 4 -5 50
-1 -1 6 -17 72
-5 -1 10 -61 360
5 -1 0 -11 0

Since f (5) = 0,   x =  5 is a zero. The depressed polynomial is   - x 2- 11 = 0

Since the depressed polynomial of this zero, - x 2- 11 , is quadratic, use the Quadratic Formula to find the roots of the related quadratic equation

image

Substitute a  = -1 , b  = 0 , c  = -11

image

image

image

Roots of the polynomial are one real root at = 5 and two imaginary roots at x = -i√11 and

x =  +i√11.

 

answered May 15, 2014 by david Expert
edited May 15, 2014 by david

Related questions

...