Question

if the sum of the roots of the equation x²-px+q=0 be m times their difference , prove that p²(m²-1)=4m²q

Answer 1

Answer:

Let the roots of equation be a & b

a+b= p

ab=q

by problem,

p=m(a-b)

squaring both sides

p^2=m^2(a-b)^2

p^2=m^2((a+b)^2-4ab)

p^2=m^2p^2-4m^2q

p^2(m^2-1)=4m^2q