Question

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

• A. zero
• B. one
• C. two
• D. three

Answer 1

Answer: (B)

one

let ,

$x^3-2x^2-x+2=0$ ___ (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.