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$f(x)$ is a monic polynomial such that $f(0)=4$ and $f(1)=10$. If $f(x)$ has degree $2$, what is $f(x)$? Express your answer in the form $ax^2+bx+c$, where $a$, $b$, and $c$ are real numbers.

michaelcai  Sep 16, 2017

Best Answer 

 #1
avatar+5249 
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A monic polynomial is a polynomial where the cofficient of the highest order term is 1. (I didn't know this until now, I had to look it up here.)

 

f(x) is a monic polynomial with a degree of 2.   So we can say...

 

f(x)    =    1x2  + bx + c    =    x2 + bx + c

 

The problem says  f(0) = 4 . So...

 

f(0)  =  02 + b(0) + c

  4   =  0   +   0   + c

  4   =  c

 

Now that we know  c = 4 , we know that  f(x) = x2 + bx + 4 .

 

The problem says f(1) = 10 . So...

 

f(1)  =  12 + b(1) + 4

10   =  1  +   b   + 4

10   =  5 + b

  5   =  b

 

Now we know  b = 5  and  c = 4 , so   f(x)  =  x2 + 5x + 4 .

hectictar  Sep 16, 2017
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1+0 Answers

 #1
avatar+5249 
+2
Best Answer

A monic polynomial is a polynomial where the cofficient of the highest order term is 1. (I didn't know this until now, I had to look it up here.)

 

f(x) is a monic polynomial with a degree of 2.   So we can say...

 

f(x)    =    1x2  + bx + c    =    x2 + bx + c

 

The problem says  f(0) = 4 . So...

 

f(0)  =  02 + b(0) + c

  4   =  0   +   0   + c

  4   =  c

 

Now that we know  c = 4 , we know that  f(x) = x2 + bx + 4 .

 

The problem says f(1) = 10 . So...

 

f(1)  =  12 + b(1) + 4

10   =  1  +   b   + 4

10   =  5 + b

  5   =  b

 

Now we know  b = 5  and  c = 4 , so   f(x)  =  x2 + 5x + 4 .

hectictar  Sep 16, 2017

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