Question 1129569
{{{x^3-qx+q+3=0 }}}

{{{x^3-q(x-1-3)=0 }}}


{{{x^3=q(x-4) }}}

{{{q=x^3/(x-4) }}} ->{{{x<>4}}}; => to have real roots, {{{x}}} must be greater than {{{4}}}

the range of values:

 ({{{4}}},{{{infinity}}})



check few of them:

{{{x=4.1}}} 

{{{q=4.1^3/(4.1-4)=689.21}}}=>{{{x^3-689.21x+689.21+3=0}}}=>{{{x^3-689.21x-692.21=0}}}


{{{ graph( 600, 600, -50, 50, -5000, 5000,x^3-689.21x-692.21) }}}

{{{x=5}}} 

{{{q=5^3/(5-4)=75}}}=>{{{x^3-75x+75+3=0}}}=>{{{x^3-75x-73=0}}}

{{{ graph( 600, 600, -30, 30, -300, 300,x^3-75x-73) }}}


{{{x=5}}} 

{{{q=6^3/(6-4)=108}}}=>{{{x^3-108x+108+3=0}}}=>{{{x^3-108x-111=0}}}

{{{ graph( 600, 600, -30, 30, -300, 300,x^3-108x-111) }}}