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

mharrigan920 Mar 16, 2020

#1**+1 **

With x = 6 as one solution we must have:

(x-6)(x^{2} + ax + b) = x^{3} - 37x + 6

or x^{3 }+ ax^{2} + bx - 6x^{2} - 6ax - 6b = x^{3} - 37x + 6

or x^{3} + (a-6)x^{2} + (b-6a)x - 6b = x^{3} - 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: x^{2} + 6x - 1 = 0

Can you take it from here?

Alan Mar 16, 2020