Question

Solve this question for me please

Answer 1

Answer:

$P(x)=\dfrac{(x-b)(x-c)}{(a-b)(a-c)}+\dfrac{(x-c)(x-a)}{(b-c)(b-a)}+\dfrac{(x-a)(x-b)}{(c-a)(c-b)}$

$\implies P(x)=\dfrac{(x-b)(x-c)}{(a-b)(a-c)}-\dfrac{(x-c)(x-a)}{(b-c)(a-b)}+\dfrac{(x-a)(x-b)}{(a-c)(b-c)}$

$\implies P(x)=\dfrac{(x-b)(x-c)(b-c)-(x-c)(x-a)(a-c)-(x-a)(x-b)(a-b)}{(a-b)(a-c)(b-c)}\\\\\textsf{Let x=a in the equation :}\\\\\implies P(a)=\dfrac{(a-b)(a-c)(b-c)-0-0}{(a-b)(a-c)(b-c)}\\\\\implies P(a)=\dfrac{(a-b)(a-c)(b-c)}{(a-b)(a-c)(b-c)}\\\\\implies P(a)=1$

Answer is OPTION A

Step-by-step explanation:

A function defined as P(x) depends on the variable x .

Here the above equation is substituted so that the steps become shot and the solution is easier .

For any value of x , the equation will be the same .

Hence substitute x=a so that we obtain the same numerator divided by the same denominator which gets cancelled.

Answer is 1 .