+0  
 
0
67
1
avatar

\(f(x) = x^2-kx+18\). One root is twice the other. Find the roots. 

 

I got 3 and 6 from this since Vieta's formula says that the product of the roots must be 18 and 3*2 = 6. Did I do it correctly? 

 Nov 15, 2020

Best Answer 

 #1
avatar+9198 
+1

Let  a  and  b  be the roots. Then we can make these two equations:

 

ab  =  18     and     a  =  2b

 

Substituting  2b  in for  a  into the first equation, we get:

 

(2b)b  =  18

 

2b2  =  18

 

b2   =   9

 

b   =   ± 3

 

Which means.....

 

a   =   2 * (± 3)

 

a   =   ± 6

 

So  3  and  6  is one possible solution,  and the other possible solution is  -3  and  -6   smiley

 Nov 15, 2020
 #1
avatar+9198 
+1
Best Answer

Let  a  and  b  be the roots. Then we can make these two equations:

 

ab  =  18     and     a  =  2b

 

Substituting  2b  in for  a  into the first equation, we get:

 

(2b)b  =  18

 

2b2  =  18

 

b2   =   9

 

b   =   ± 3

 

Which means.....

 

a   =   2 * (± 3)

 

a   =   ± 6

 

So  3  and  6  is one possible solution,  and the other possible solution is  -3  and  -6   smiley

hectictar Nov 15, 2020

21 Online Users

avatar