If x1, x2, x3, , xn are the roots of polynomial x^n + ax + b - Maths - Limits and Derivatives

Question

If x1, x2, x3, , xn are the roots of polynomial x^n + ax + b = 0,
then the value of (x1 - x2)(x1 - x3)(x1 - x4) (x1 - xn) is equal to

Brijendra Pal · Accepted Answer

Hi, if x1, x2, x3,
xn are the roots of polynomial xn+ax+b=0 then  xn+ax+b=x-x1x-x2x-x3
x-xnx-x2x-x3
x-xn= xn+ax+bx-x1putting x = x1x1-x2x1-x3
x1-xn=limx→x1 xn+ax+bx-x1now since x1 is roots of  xn+ax+b so it will tends to zero and so does the denomiantorso it is0/0 form so using L'hospital rule= limx→x1 ddxxn+ax+bddxx-x1=limx→x1nxn-1+a1= nx1n-1+a  Answer

If x1, x2, x3, ... , xn are the roots of polynomial x^n + ax + b = 0, then the value of (x1 - x2)(x1 - x3)(x1 - x4)...(x1 - xn) is equal to