If the sum of two roots of x:4+2x:3−8x:2−18x−9=0 is 0, find the roots of the equation

iroroPagbublh

iroroPagbublh

Answered question

2022-08-13

If the sum of two roots of
x 4 + 2 x 3 8 x 2 18 x 9 = 0
is 0, find the roots of the equation

Answer & Explanation

Payton Mcbride

Payton Mcbride

Beginner2022-08-14Added 18 answers

Generally, if there's two roots whose sum is zero, then it means that two factors are x−a and x+a, which means that x 2 a 2 must be a factor. So clearly
( x 2 a 2 ) ( x 2 + b x + c ) = x 4 + 2 x 3 8 x 2 18 x 9 = 0
Find the values of a 2 , b, and c that satisfy the left equality, and you'll have found factors that you can then solve for all roots. (This works even if there's no rational root)

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