+0  
 
+1
407
1
avatar+598 

$f(x)$ 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+7324 
+2

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
 #1
avatar+7324 
+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

25 Online Users

avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.