Fitzpatrick Polynomials (1 Viewer)

[Soulful]

This question is from exercise 27d) of Fitzpatrick and omg the whole section is so goddamn hard but this one has really just stopped me from doing anything else

Solve 6x^4 - 11x^3 -26x^2 +22x + 24 = 0 given that the product of two of its roots is equal to product of the other two.

I've changed the roots to a, b, c and (ab/c) and tried solving from their but nothing seems to be working

PLEASE HELP :'( :'(

 

[Soulful]

bump! :'(

 

[Squar3root]

how you changed the product of the roots is wrong; try again

EDIT:
My answer is: (2x -3)(3x-4)(x^2 -2x-2)

 

[Squar3root]

OP; you'll get it out. just need the right starting point

 

[integral95]

I've changed the roots to a, b, c and (ab/c) and tried solving from their but nothing seems to be working

PLEASE HELP :'( :'(

you got that wrong, let the roots be a,b,c,d and ab=cd

and as the other said use all of the root properties of the polynomial

 

[Squar3root]

you got that wrong, let the roots be a,b,c,d and ab=cd

and as the other said use all of the root properties of the polynomial

this is the right starting point

 

[Soulful]

this is the right starting point

hahahah fuck :'(

time to stop doing maths late at night

thanks everyone