JEE Mains · Maths · STD 12 - 1. relation and function
Let \(f ( x )\) be a quadratic polynomial with leading coefficient \(1\) such that \(f(0)=p, p \neq 0\) and \(f(1)=\frac{1}{3}\). If the equation \(f(x)=0\) and \(fofofof (x)=0\) have a common real root, then \(f(-3)\) is equal to \(........\)
- A \(25\)
- B \(24\)
- C \(23\)
- D \(22\)
Answer & Solution
Correct Answer
(A) \(25\)
Step-by-step Solution
Detailed explanation
Let \(f(x)=(x-\alpha)(x-\beta)\) It is given that \(f(0)=p \Rightarrow \alpha \beta=p\) and \(f(1)=\frac{1}{3} \Rightarrow(1-\alpha)(1-\beta)=\frac{1}{3}\) Now, let us assume that \(\alpha\) is the common root of \(f(x)=0\) and \(f \circ f \circ f o f(x)=0\) \(fofofof(x)=0\)…
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