Question

obtain the double root of the equ x3-x2-x+1=0
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Answer 1

Step-by-step explanation:

We have to solve for x: x^3+x^2+x+1=0

x^3+x^2+x+1=0

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

=> (x^2+1)(x+1)

x+1=0

x=1=0

x= -1

=> x^2=1

x= i , i

Answer 2

Therefore, roots of equation x³-x²- x + 1 = 0 are (1, 1, -1)

and the double root is 1

Given:

Equation x³-x²- x + 1 = 0

To find:

Double roots of given equation x³-x²- x + 1 = 0  

Solution:

We can find the roots of the equation by factorising

Now we will factorise the given equation

⇒ x³- x²- x + 1 = 0

⇒ x²(x - 1) - (x - 1) = 0       [ take x² common ]

⇒ (x -1) (x² - 1) = 0            [ take (x -1) common ]

⇒ (x - 1 ) (x+1) (x-1) = 0      [ From (a-b)² = (a+b) (a-b) ]

⇒ x - 1 = 0 ⇒  x = 1

⇒ x + 1 = 0 ⇒ x = -1

⇒ x - 1 = 0 ⇒ x = 1

Therefore, roots of equation x³-x²- x + 1 = 0 are (1, 1, -1)

and the double root is 1

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