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Question-193962




Question Number 193962 by Abdullahrussell last updated on 24/Jun/23
Answered by AST last updated on 24/Jun/23
⇒f(x)=Q(x)(x−a)(x−b)+R⇒f(a)=R,f(b)=R  ⇒((f(a)(x−b)−f(b)(x−a))/(a−b))=((R(x−b−x+a))/(a−b))=R
$$\Rightarrow{f}\left({x}\right)={Q}\left({x}\right)\left({x}−{a}\right)\left({x}−{b}\right)+{R}\Rightarrow{f}\left({a}\right)={R},{f}\left({b}\right)={R} \\ $$$$\Rightarrow\frac{{f}\left({a}\right)\left({x}−{b}\right)−{f}\left({b}\right)\left({x}−{a}\right)}{{a}−{b}}=\frac{{R}\left({x}−{b}−{x}+{a}\right)}{{a}−{b}}={R} \\ $$
Answered by cortano12 last updated on 24/Jun/23
$$\:\:\:\:\underbrace{\:}\: \\ $$

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