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what is the sum of the roots of the polynomial shown below

0 votes

f(x)=3x^3+12x^2+3x-18

asked Jul 11, 2013 in ALGEBRA 2 by angel12 Scholar

2 Answers

0 votes

Given that

image

Substitute the value of x=1

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f(1) = 0

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That means  (x-1) is a factor for the given equation

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Take 3 common

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3 is also a factor

image

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Take (x+3) common

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The remaining factors are (x+2) (x+3)

The  factors the given polynomial is (x-1) (x+2) (x+3)

Therefore the  roots of the given polynomial is (x-1) = 0 ==> x = 1

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

                                                                       (x+3) = 0 ==> x = -3

The sum of the roots are 1 - 2 - 3 = -4

 

answered Jul 11, 2013 by jouis Apprentice
0 votes

The polynomial is f (x) = 3x3 + 12x2 + 3x - 18.

Sum of the roots of the third degree polynomial = - x2 coefficient / x3 coefficient.

Here, x2 coefficient = 12 and x3 coefficient is 3.

Therefore, sum of the roots of the given polynomial = - 12/3 = - 4.

answered Aug 5, 2014 by lilly Expert

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