+0  
 
-1
104
1
avatar+318 

Thanks!!!

Find all rational zeros of f. Then use the depressed equation to find all roots of the equation f(x)=0.

 

f(x)=x^3-37x+6

 

** i got the answer that 6 is the rational zero but not sure with second part of problem

 Mar 16, 2020
 #1
avatar+30595 
+1

With x = 6 as one solution we must have:

 

(x-6)(x2 + ax + b) = x3 - 37x + 6

 

or x+ ax2 + bx - 6x2 - 6ax - 6b = x3 - 37x + 6

 

or x3 + (a-6)x2 + (b-6a)x - 6b = x3 - 37x + 6

 

So we must have a = 6 and b = -1 for the LHS to equal the RHS.

 

The depressed equation is thus the quadratic: x2 + 6x - 1 = 0

 

Can you take it from here?
 

 Mar 16, 2020

29 Online Users

avatar
avatar