Polynomials Question (1 Viewer)

[ConHeo97]

Not really sure on how to go about doing this : /
Solve the equation 6x⁴-11x³-26x²+22x+24=0 given that the product of two of the roots is equal to the product of the other two.

 

[rumbleroar]

let your roots be a, b, c, d

where ab = cd

so, sum of roots a+b+c+d = 11/6
sum of couples: ab + ac + ad + bc + bd + cd = -26/6
sum of threes: abc + abd + acd + bcd = -22/6
product of roots: abcd = 4

here, sub ab = cd into the product of roots so you get:
(cd)cd = 4
i.e. cd = 2, thus ab = 2

sub this into the other forumlas and keep on simplifying and reducing. you can also use the fact a = 2/b or c=2/d (and the reversals) to get things in terms of one subject, etc.

hope that helps

 

[ConHeo97]

thanks mate