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AP EAMCET2003MathematicsQuadratic Equation

Let a 0 and p(x) be a polynomial of degree greater than 2. If p(x) leaves remainders a and -a when divided respectively by x+a and x-a , then the remainder when p(x) is divided by x^2-a^2 is :

Options

  1. Ax
  2. B-x
  3. C-2 x
  4. D2 x

Correct answer

B. -x

Step-by-step solution

Let the remainder be R(x) , then R(x)=P(x)+q Given, R(-a)=a -P a+q=a (i) and R(a)=-a P a+q=-a (ii) On solving Eqs. (i) and (ii), we get P=1, q=0 R(x)=-x

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