What are the possible rational roots of x^3-2x^2+x+18=0 and then determine the rational roots?

Donte Holder

Donte Holder

Answered question

2023-03-12

What are the possible rational roots of x 3 - 2 x 2 + x + 18 = 0 and then determine the rational roots?

Answer & Explanation

Mikaela Horn

Mikaela Horn

Beginner2023-03-13Added 6 answers

Only possible rational roots are ± 1 , ± 2 , ± 3 , ± 6 , ± 9 , ± 18
x 3 - 2 x 2 + x + 18 = ( - 2 ) 2 - 2 ( - 2 ) 2 + ( - 2 ) + 18
x 3 - 2 x 2 + x + 18 = 0
x 3 - 2 x 2 + x + 18 = ( x + 2 ) ( x 2 - 4 x + 9 )
x 2 - 4 x + 9
Δ = b 2 - 4 a c = ( - 4 ) 2 - 4 ( 1 ) ( 9 ) = 16 - 36 = - 20
Δ < 0 , there are no real zeros and no linear factors
0 = x 2 - 4 x + 9
0 = ( x - 2 - 5 i ) ( x - 2 + 5 i )
Roots are x = 2 ± 5 i

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