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

774,916 users

2x^4 - 5x^3 - 11x^2 + 20x + 12; -2, 3 find roots of polynomials.

0 votes

please  help!

asked Feb 24, 2014 in ALGEBRA 2 by harvy0496 Apprentice

2 Answers

0 votes

image

Solve by using synthetic division.

Given roots of the equation image.

image

The quotient is image.

Solve for roots

image.

image

image

image

image

The roots of the polynomial are image

answered Apr 9, 2014 by Johncena Apprentice
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.

Rational Root Theorem, if a rational number in simplest form p/q is a root of the polynomial equation anx n + an  1x n – 1 + ... + a1x + a0 = 0, then p is a factor of a0 and q is a factor if an.

The polynomial is 2x 4 - 5x 3 - 11x 2+ 20x + 12.

If p/q is a rational zero, then p is a factor of 12 and q is a factor of 2.

The possible values of p are   ± 1,   ± 3, and ± 4.

The possible values for q are ± 1, ± 2.

By the Rational Roots Theorem, the only possible rational roots are, p/q = ± 1, ± 1/2, ± 3/2, ± 2, ± 3, and ± 4.

Make a table for the synthetic division and test, wheather - 2 is a possible real zero or not.

p/q

2

- 5

- 11

20

12

- 2

2

- 9

7

6

0

Since, f(- 2) = 0, x = - 2 is a zero. The depressed polynomial is  2x 3 - 9x 2 + 7x + 6 = 0.

If p/q is a rational zero, then p is a factor of 6 and q is a factor of 2.

By the Rational Roots Theorem, the only possible rational roots are, p/q = ± 1, ± 1/2, ± 3/2, ± 2, and ± 3.

Make a table for the synthetic division and test, wheather 3 is a possible real zero or not.

p/q

2

- 9

7

6

3

2

- 3

- 2 0

Since, f(3) = 0, x = 3 is a zero. The depressed polynomial is  2x 2 - 3x - 2 = 0.

By factor by grouping.

2x 2 - 4x + x - 2 = 0

2x(x - 2) + 1(x - 2) = 0

Factor : (x - 2)(2x + 1) = 0

Apply zero product property.

x - 2 = 0 and 2x + 1 = 0

x = 2 and x = - 1/2.

Therefore, the roots of the polynomial are x = - 2, x = 3, x = 2, and x = - 1/2.

answered May 15, 2014 by lilly Expert

Related questions

...