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Basic Concepts Of Determinant Part 3

Posted on - 04-01-2017

Math

IIT JEE

Differentiation of a Determinant

  • where a dash denotes derivative with respect to x.

    Example.1

    Let a be a repeated root of the quadratic equation f(x) =0 and A(x), B(x), C(x) be polynomials of degree 3,4, and 5 respectively. Then show that is divisible by f(x), where a dash denotes the derivative, with respect to x.

    Solution

    Let g(x) =

    We find that g(a)=0, & g'(a)=0


    &⇒
    g(x)=(x-a)2 P(x), where P(x) is a polynomial of degree 3
    . Also f(x)=0 is a quadratic equation having repeated root a .


    &⇒
    g(x) is divisible by f(x).

     
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