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Grade: 12th pass

                        

Find an interval in which root of the equation x3-2x-1 =0 lie?

2 years ago

Answers : (1)

Susmita
425 Points
							
You see if we take x=-1 then the left hand side becomes zero.
So x+1=0.Following this rule we shall factorize the equation.
x3-2x-1=0
Or,x3+x2-x2-x-x-1=0
or,x2(x+1)-x(x+1)-1(x+1)=0
Or,(x+1)(x2-x-1)=0
so either x=-1 or 
x=\frac{1 \pm \sqrt{1+4} }{2}=\frac{1 \pm\sqrt{5}}{2}
So the roots lie between -1 to (1+root5)/2.
Please approve the answer if you are helped.
2 years ago
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