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 sim

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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 sim

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
A. 1
B. x
C. `(x^(2)+(a+b+c)(ab+bc+ca))/((a-b)(b-c)(c-a))`
D. 0

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - A
`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))`
`"Let "P(a)=1+0+0=1`
`P(b) =0+1+0=1`
`P (c) =0+0+1=1`
`:. P(x)=1 " for all "x in R`.

5 views Answered 2023-02-05 15:29