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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.

tertre  Jun 2, 2017
 #1
avatar+86859 
+2

 

A monic polynomial has a lead coefficient of 1......so a  = 1

 

And  since f(0)  = 4, then c  = 4

 

So  all we need to do is solve for b

 

f(1)  = 10   ....    so   ......

 

(1)^2  + b(1)  +  4  = 10

1  + b + 4   =  10

b  = 5

 

So.....our function is

 

f(x)   = x^2  + 5x  +  4

 

 

cool cool cool

CPhill  Jun 2, 2017

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