How to find the rational roots of x^4+3x^3+3x^2-3x-4=0?

chichogpw4y

chichogpw4y

Answered question

2023-02-13

How to find the rational roots of x 4 + 3 x 3 + 3 x 2 - 3 x - 4 = 0

Answer & Explanation

lew3i0

lew3i0

Beginner2023-02-14Added 4 answers

x 4 + 3 x 3 + 3 x 2 - 3 x - 4 = ( x - 1 ) ( x 3 + 4 x 2 + 7 x + 4 )
x 3 + 4 x 2 + 7 x + 4 = ( x + 1 ) ( x 2 + 3 x + 4 )
The discriminant Δ = b 2 - 4 a c = 3 2 - ( 4 × 1 × 4 ) = 9 - 16 = - 7
Only possible rational roots ± 1 , ± 2 , ± 4

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