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One factor of F(x)=x^3-14x^2+61x-84 is (x-7) what are the zeros of the function

 Mar 25, 2020
 #1
avatar+111330 
+1

Since (x - 7) is a factor   then 7 is a zero

 

Using a little  synthetic  division to find the  remaining polynomial we have that

 

7  [ 1    -14       61      -84   ]

               7      -49       84

     ______________________

       1      -7      12        0

 

The remaining polynomial  is

 

x^2   -7x  +  12

 

Set to  0  and factor and we have that

 

(x - 3) (x - 4)  =  0

 

Setting each factor to 0  and solving for x  gives the other two roots  (zeroes)  of  x = 3  and  x = 4

 

 

 

cool cool cool

 Mar 25, 2020
 #2
avatar+1970 
+2

Nice, Chris!

CalTheGreat  Mar 25, 2020

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