Question

If the sum of the roots of a quadratic equation is 2 and the sum of their cubes is 27, then the equation is ?

Answer 1

so given

a+b=2

&

a³+b³=27

(a+b)³-3ab (a+b)=27

2³-3ab ×2=27

-6ab=27-8

ab =-19/6

the required equation =

x²-(a+b)x+ab =0

x²-2x-19/6=0