Question

Number of common roots of the equation $$\displaystyle x^{3}-2x^{2}-x+2=0$$ and $$\displaystyle x^{3}+6x^{2}+11x+6=0$$ is

A
zero
B
one
C
two
D
three

Solution

The correct option is A onelet ,$$x^{3}-2x^{2}-x+2=0$$ ___ (1)$$x^{3}+6x^{2}+11x+6=0$$___(2)now put x=1 in eq (1)$$=1^{3}-2\times 1^{2}-1+2$$$$=1-2-1+2\Rightarrow 0$$put x=1 in eq (2)$$=1^{3}+6\times 1^{2}+11\times 1+6$$$$=1+6+11+6\Rightarrow 24$$so x=1 is not a common root of both equations.now put x=-1 in eq (1)$$=-1^{3}-2\times -1^{2}+1+2$$$$=-1-2+1+2\Rightarrow 0$$put x=-1 in eq (2)$$=-1^{3}+6\times -1^{2}+11\times -1+6$$$$=-1+6-11+6\Rightarrow 0$$With similar $$x=\pm 2$$ puts in both equations has no common roots finds.$$\therefore x=-1$$ is the common roots of the equations.Maths

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