Quadratic polynomial

Algebra Level pending

Consider a quadratic function\(f(x)=a x^2+b x+c\) where \(a,b,c \in R\) are real no.'s and \(a\) is a non zero number and satisfy the following condition.

\((i)\) \(f(x-4)=f(x-2)\) and \(f(x)\geq x\) where \(x\in R\) .

\((ii)\) \(f(x)\leq (\frac{x+1}{2})^2\) where \(x \) \(\in\) \((0,2)\)

\((iii)\) The minimum value of \(f(x)\) is zero

\(Q-1\). The value of leading coefficient of quadratic polynomial is?

\(Q-2 \). \(f'(1)\) has the value equal to?

If the answers of \(Q-1\) and \(Q-2\) are \('a'\) and\( 'b'\) respectively then the value of \(a\times b\) is

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