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Suppose a,b,c are three distinct real numbers.Let P(x)= (x-b)(x-c) / (a-b)(a-c) + (x-c)(x-a) / (b-c)(b-a) + (x-a)(x-b) / (c-a)(c-b) When simplified P(x) becomes

Suppose a,b,c are three distinct real numbers.Let
P(x)= (x-b)(x-c) / (a-b)(a-c) + (x-c)(x-a) / (b-c)(b-a) + (x-a)(x-b) / (c-a)(c-b)
When simplified P(x) becomes

Grade:10

2 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
P(x)=(x-b)(x-c)/(a-b)(a-c) + (x-c)(x-a)/(b-c)(b-a) + (x-a)(x-b)/(c-a)(c-b)
=(x-a)(x-b)(x-c)/(a-b)(b-c)(c-a)[(c-b)/(x-a) +(a-c)/(x-b)+(b-a)/(x-c)]
Thanks & Regards
Rinkoo Gupta
AskIITians Faculty
Sridhar
11 Points
5 years ago
let x=a,
then, substituting in the given equation,
p(x)=1+0+0=1
similarly, p(x where x=b)=1, p(x where x=c)=1
thus, generalized answer can be taken as 1.

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