Question 796422
given: {{{P(x) = 4x^4 -x^3 -28x^2 - 17x + 6}}}, {{{c = 1/4}}}, {{{c=-2}}}


{{{0=4x^4 -x^3-28x^2 -17x + 6}}}
...
{{{c = 1/4}}}
{{{4c = 1}}}
{{{4c - 1 = 0}}} => {{{(4x-1)}}}
...{{{c = -2}}}
{{{c + 2 = 0}}} => {{{(x+2)}}}
...
{{{(4x-1)(x+2)}}}

From the given zeros we know
{{{4x^2+7x-2}}}
...
To find the remaining factors, divide
{{{(4x^4 -x^3 -28x^2 -17x + 6)/(4x^2+7x-2)=0}}}........factor both numerator and denominator
...
{{{((4 x-1) (x+1) (x+2) (x-3))/((4x-1)(x+2))=0}}}......simplify

{{{(cross((4 x-1)) (x+1)cross( (x+2)) (x-3))/(cross((4x-1))cross((x+2)))=0}}}

{{{ (x+1) (x-3)=0}}}

All four zeros:

{{{1/4}}}, {{{- 2}}} : given
{{{3}}}, {{{-1}}} : solved

so, 

{{{x= -2}}} (smallest value)
{{{x=3}}} (largest value)


{{{ graph( 600, 600, -10, 10, -10, 10, 4x^4 -x^3 -28x^2-17x + 6) }}}