Question

Alfa ,bita, gama are the zeroes of the cubic polynomial x3–2x+qx-r if Alfa +bita =0 then proove 2q=r​

Answer 1

2q-r

Step-by-step explanation:

x³-2×+qx²-r

zeroes are alpha,beeta,gama

alpha+beeta+gama= -b/a

alpha.beeta +beeta.alpha + alpha.gama= c/a

alpha.beeta.gama = -d/a ( a=1,b= -2,c=q,d= -r)

for simplification, alpha= m, beeta = n, gama = z

m +n+z = 2

z =2 ( given: alpha + beeta=0) ------- (1)

mnz = r

mn.2=r ( from 1 )

mn= r/2---------(2)

mn+nz+zm= q

r/2 + z( n +m)= q

r/2 + 0= q( given)

r = 2q

Hence proved