Mathematics - Determinant Question with Solution | TestHub

$$\begin{array}{rl}& f(x)=\left|\begin{array}{ccc}1+\left(a^2+b^2+c^2+2\right)x& \left(1+b^2\right)x& \left(1+c^2\right)x\\ 1+\left(a^2+b^2+c^2+2\right)x& 1+b^{2}x& \left(1+c^2\right)x\\ 1+\left(a^2+b^2+c^2+2\right)x& \left(1+b^2\right)x& 1+c^{2}x\end{array}\right|\text{, Applying }{C}_1\to C_1+C_2+C_3\\ & =\left|\begin{array}{ccc}1& \left(1+b^2\right)x& \left(1+c^2\right)x\\ 1& 1+b^{2}x& \left(1+c^2\right)x\\ 1& \left(1+b^2\right)x& 1+c^{2}x\end{array}\right|\because a^2+b^2+c^2+2=0\\ & f(x)=\left|\begin{array}{ccc}0& x-1& 0\\ 0& 1-x& x-1\\ 1& \left(1+b^2\right)x& 1+cx\end{array}\right|;\text{ Applying }{R}_1\to R_1-R_2,R_2\to R_2-R_3\\ & f(x)=(x-1{)}^2\end{array}$$ Hence degree $=2$.