WBJEE · Maths · Quadratic Equation
Let \(p(x)\) be a quadratic polynomial with constant term 1. Suppose \(p(x),\) when divided by \(x-1\) leaves remainder 2 and when divided by \(x+1\) leaves remainder \(4 .\) Then, the sum of the roots of \(p(x)=0\) is
- A -1
- B 1
- C \(-\frac{1}{2}\)
- D \(\frac{1}{2}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
Let \(\quad p(x)=a x^{2}+b x+c\) Given, constant term 'c' \(=1\) \(\therefore \quad p(x)=a x^{2}+b x+1\) Now, by given condition, \(p(1)=2\) (remainder) \(\begin{array}{lr}\Rightarrow & a+b+1=2 \\ \Rightarrow & a+b=1\end{array}\)…
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