polynomials help! (1 Viewer)

[fahadmumtaz88]

the quadratic equation x^2 -5x +8 = 0 has alpha and beta as roots. Find the equation whose roots are alpha/beta and beta/alpha.

Thanks

 

[SeDaTeD]

well, its a quadratic obviously. product of roots = 1, sum of roots is a/b + b/a = (a^2 + b^2)/ab. you can find the values of a^2 + b^2 = (a+b)^2 - 2ab, and of ab from the original eqn (sum and products of roots).

 

[lucifel]

you could always do this instead:

a/b = ab/b^2
b/a = ab/a^2

and you know what ab is, (from product of roots)
so let y = 8/x^2 and sub it in.