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Solve the equation x^3 - 2x^2 - x + 2 = 0

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macaronomy | Student, Grade 10 | eNotes Newbie

Posted June 1, 2010 at 12:43 AM via web

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Solve the equation x^3 - 2x^2 - x + 2 = 0

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giorgiana1976 | College Teacher | Valedictorian

Posted June 1, 2010 at 12:44 AM (Answer #1)

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To solve the equation, we'll group the first 2 terms together and the next 2 terms together, so that we can factorize:

(x^3 - 2x^2) - (x - 2) = 0

x^2(x - 2) - (x - 2) = 0

We'll factorize again:

(x - 2)(x^2 - 1) = 0

We'll put each factor as being 0.

x-2 = 0

x = 2

x^2 - 1 = 0

The expression is a difference of squares:

x^2 - 1 = (x - 1)(x + 1) = 0

x-1 = 0

x = 1

x + 1 = 0

x = -1

The solutions of the equation are: {-1,1,2}.

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neela | High School Teacher | Valedictorian

Posted June 1, 2010 at 12:47 AM (Answer #2)

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To solve x^3-2x^2-x+2 = 0.

Solution:

Grouping  as

x^2(x-2)-1(x-2) = 0. Or

(x-2)(x^2-1) = 0. Or

(x-2)(x+1)(x-1) = 0, as x^2-1 = x^2-1^2 = (x+1)(x-1).

So x-2= 0, Or x+1 = 0, Or x-1) = 0. From these 3 equations, we get:

x=2,

x=-1  and

x= 1.

 

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adarshanurag | Student, Grade 11 | Valedictorian

Posted January 22, 2014 at 3:57 PM (Answer #3)

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x^3-2x^2-x+2 = 0

Solution......

x^2(x-2)-1(x-2) = 0 

=>(x-2)(x^2-1) = 0

=>(x-2)(x+1)(x-1) = 0                        [x^2-1 = x^2-1^2 = (x+1)(x-1)]

=> x-2=0        I      =>  x+1=0      I    =>   x-1=0

=>x=2            I      =>  x=-1         I    =>   x=1

Hence x={2,-1,1}

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atyourservice | TA , Grade 10 | Valedictorian

Posted February 23, 2014 at 1:58 AM (Answer #4)

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`x^3 - 2x^2 - x + 2 = 0`

You can solve by factoring

`(x^3 - 2x^2) (- x + 2)`

`x^2(x-2) -1(x-2)`

`(x^2-1) (x-2)`

x-2=0     x=2

`x^2-1 = (x-1)(x+1) = 0`

`x=1 x=-1`

x=1      x=-1    x=2

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fashionableb1 | TA , Grade 10 | Salutatorian

Posted March 6, 2014 at 5:34 PM (Answer #5)

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`x^3 - 2x^2 - x + 2 = 0 `

group the factors

`(x^3 - 2x^2) (- x + 2)  `

take out the numbers the numbers in the parentheses have in common

`x^2(x-2) -1(x-2) `

`(x^2-1)(x-2) `

set those parenthesis equal to 0

x-2=0

`x=2`

`x^2-1=o`

`x^2=1`

`x=+-1`

`x=1 x=-1`

so x is 1,-1 and 2

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