Number of roots common to the equations \(x^3+x^2-2 x-2=0\) and \(x^3-x^2-2 x+2=0\) is
Number of roots common to the equations \(x^3+x^2-2 x-2=0\) and \(x^3-x^2-2 x+2=0\) is
1
2
3
0
Solution
Let \(x\) is the common root of the equations
\(x^3+x^2-2 x-2=0 \text { and } x^3-x^2-2 x+2=0\)
So, \(\alpha\) will satisfy both the equations
\(\begin{array}{ll}
\text {Now, } & \alpha^3+\alpha^2-2 \alpha-2=0 \\
\text {and } & \alpha^3-\alpha^2-2 \alpha+2=0
\end{array}\)
On subtraction, we get
\(2 \alpha^2-2=0 \Rightarrow \alpha= \pm 1.\)
So, there are 2 common roots.