2. Solved Papers
  3. VIT Engineering

VIT Engineering VIT Engineering Solved Paper-2010

  • question_answer
    If \[f(x),\,g(x)\]and \[h\,(x)\]are three polynomials of degree 2 and \[\Delta (x)=\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\] then \[\Delta (x)\]is a polynomial of degree

    A)  2

    B)  3

    C)  0

    D)  atmost 3

    Correct Answer: C

    Solution :

    Since, \[f(x),\] \[g(x)\] and \[h(x)\] are the polynomials of degree 2, therefore, \[f\,\,(x)=g\,\,(x)=h\,\,(x)=0\] Now, \[\Delta \,x=\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\] \[\Rightarrow \] \[\Delta \,x=\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\] \[+\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\]       \[+\left| \begin{matrix}    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\    f(x) & g(x) & h(x)  \\ \end{matrix} \right|\] \[\Rightarrow \] \[\Delta (x)=0+0+0=0\] \[\Rightarrow \] \[\Delta (x)=\text{constant}\] Thus, \[\Delta (x)\]is the polynomial of degree zero.


You need to login to perform this action.
You will be redirected in 3 sec spinner