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Let $f(x)$ be a monic polynomial such that $f(0)=4$ and $f(1)=8$. If $f(x)$ has degree $2$, what is $f(x)$? Enter your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers.

 Aug 18, 2023
 #1
avatar+128406 
+1

We have

 

a*0^2 + b*0 + c = 4       so  c   =  4

 

and

 

a*1^2  + b*1  + 4 =  8

a + b =  4

Since it is  monic  a = 1  and  b =3

 

So

 

f(x)  =  x^2  + 3x  + 4

 

 

cool cool cool

 Aug 18, 2023

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