TS EAMCET · Maths · Quadratic Equation
Let \(a \neq 0\) 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 :
- A \(x\)
- B \(-x\)
- C \(-2 x\)
- D \(2 x\)
Answer & Solution
Correct Answer
(B) \(-x\)
Step-by-step Solution
Detailed explanation
Let the remainder be \(R(x)\), then \(R(x)=P(x)+q\) Given, \(\quad R(-a)=a \Rightarrow-P a+q=a\) \(\ldots\) (i) and \(R(a)=-a \Rightarrow P a+q=-a$$\ldots\) (ii) On solving Eqs. (i) and (ii), we get \(P=1, q=0\) \(\therefore \quad R(x)=-x\)
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