Question

4 + 3b3 - 7b2 - 27Ь - 18 = 0
list all the possible rational roots using Rational root Theorem​

Answer 1

Answer:

huge gvioigndfniij cubicle

Answer 2

Given :  4 + 3b³ - 7b² - 27Ь - 18 = 0

To Find : list all the possible rational roots using Rational root Theorem​

Solution:

4 + 3b³ - 7b² - 27Ь - 18 = 0

=> 3b³ - 7b² - 27Ь - 14 = 0

All rational solutions of f(x) = 0 , where

f(x) =aₙxⁿ + aₙ₋₁xⁿ⁻¹  + . + .  + a₁x  + a₀  is a polynomial function with integer coefficients, have the following form:

p/q  = factor of constant term a₀ /  factor of leading coefficient  aₙ

a₀ = - 14

factor of  - 14  p =   ±1  , ±2  , ±7 , ±14

aₙ = 3

factor of  3  , q = ±1 , ±3

all the possible rational roots

p/q  = ±1/1  , ±1/3  , ±2/1  , ±2/3  , ±7/1  , ±7/3  , ±14/1 , ±14/3

if  Polynomial is  b⁴ + 3b³ - 7b² - 27Ь - 18 = 0

then p  =  ±1  , ±2  , ±3 , ±6 , ±9 , ±18

q = ±1

all the possible rational roots

p/q  = ±1/1  , ±2/1  , ±3/1  , ±6/1  , ±9/1  , ±18/1  

=  ±1   , ±2  , ±3   , ±6   , ±9   , ±18  

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