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Question Number 128458 by SLVR last updated on 07/Jan/21

Commented by BHOOPENDRA last updated on 07/Jan/21

$$Givenf\left(f\left(1\right)\right)=0,f\left(f\left(2\right)\right)=0$$$$i.eequationf\left(x\right)=0$$$$hastworootf\left(1\right)andf\left(2\right)$$$$f\left(1\right)+f\left(2\right)=-\alpha andf\left(1\right).f\left(2\right)=\beta$$$$so5+3\alpha +2\beta =-\alpha$$$$and(1+\alpha +\beta )(4+2\alpha +\beta )$$$$\Rightarrow 2\alpha +\beta =-\frac{5}{2}$$$$\Rightarrow (1-\frac{5}{4}-\frac{\beta }{2})(4-\frac{5}{2})=\beta$$$$\Rightarrow \beta =-\frac{3}{2}$$$$\therefore f\left(0\right)=\beta =-\frac{3}{2}$$$$$$

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