Question

Find a first degree polynomial with p(1)=6 and p(2)=10

Answer 1

Answer:

The answer is $p(x)=4x+2$

Step-by-step explanation:

Let $p(x)=ax+b$

Given $p(1)=6$

         $\Rightarrow a(1)+b=6\Rightarrow a+b=6...(1)$, replace x by 1 in p(x)

And $p(2)=10$

         $\Rightarrow a(2)+b=10\Rightarrow 2a+b=10...(2)$, replace x by 2 in p(x)

Now subtract (1) from (2)

      $\Rightarrow (2a+b)-(a+b)=10-6\\\Rightarrow a=4$

Using (1) $b=6-a=6-4=2$

So the polynomial is $p(x)=4x+2$