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The equation x^3 - x^2 + mx + 1 = 0 has two equal real roots, distinct from the third root.  Find the value of m.

 Dec 11, 2019
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x^3 - x^2  +  mx  +  1

 

By inspection, we can determine that   m  =  -1  because

 

x^3  - x^2  - 1x  +  1   =  0

 

x^2(x - 1) - 1 ( x - 1)   =  0

 

(x - 1) (x^2  - 1)   = 0

 

(x - 1) ( x - 1) ( x + 1)  =  0

 

Setting each factor to 0   and solving for x  gives the two  equal roots  of  x  =  1    and the other root x  =  - 1

 

 

cool cool cool

 Dec 11, 2019

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