Question

If x^3 + pX + q =0 has two equal roots then find 4p^3+27q^2

Answer 1

Answer:-
suppose α is the double root of x³+px+q=0

then sum of roots of x³+px+q=0 is given by -1* coefficient of x²

let β be the thir root of the given equation

then 2α+β=coefficien -1*0=0

so β=-2α

Double sum of roots of x³+px+q=0 is given by coefficient of x

so α² +αβ+βα=p

But β=-2α

so α² -4α²=p

-3α² =p

-108α⁶=4p³-----1

Product of roots of given equation is given by -1*constant term

so α² *-2α=-q

2α³=q

108α⁶=27q²---2

Adding eq 1 and eq 2

4p³ + 27q²=0

ALL THE best