Question

let p(x) be linear polynomial for which p(6)-p(2)=12 .the value of p(12)-p(2)

Answer 1

the answer is p(6)
hope it will help

Answer 2

Answer:  The required value is 30.

Step-by-step explanation:  Given that p(x) is a linear polynomial for which

$p(6)-p(2)=12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

We are to find the value of $p(12)-p(2).$

Let the linear polynomial be

$p(x)=ax+b.$

So, from equation (i), we have

$p(6)-p(2)=12\\\\\Rightarrow (a\times 6+b)-(a\times 2+b)=12\\\\\Rightarrow 6a-2a=12\\\\\Rightarrow 4a=12\\\\\Rightarrow a=\dfrac{12}{4}\\\\\Rightarrow a=3.$

So, equation (i) implies that

$p(x)=3x+b.$

Therefore, we get

$p(12)-p(2)=(3\times12+b)-(3\times2+b)=36+b-6-b=30.$

Thus, the required value is 30.