question_answer

Given that \[x=2\]is a solution of \[{{x}^{3}}-7x+6=0.\]The other solutions are_____.

A)  -1, 3                            

B)  1,-3                 

C)  1,-2                 

D)         -1,-2    

Correct Answer: B

Solution :

Let,\[f(x)={{x}^{3}}-7x+6\]and \[g(x)=x-2\]M Now, by long division method, we have \[\therefore \]\[(x-2)({{x}^{2}}+2x-3)=0\] For other solutions, \[{{x}^{2}}+2x-3=0\] \[\Rightarrow \]\[{{x}^{2}}+3x-x-3=0\Rightarrow (x+3)(x-1)=0\] \[\Rightarrow \]\[x=-3\]or 1