Question

When two equations x^2+a1x+b1=0 and x^2+a2x+b2=0 have equal root (x-k) then find k?

Answer 1

x2+a1x+b1=0------------eq(1)

x2+a2x+b2=0-------------eq(2)

equal root x-k=0   => x=k is one root

f(k) in eq (1) and eq(2)

k2+a1k+b1=k2+a2k+b2

k(a1-a2)=b2-b1

k=(b2-b1)/(a1-a2)