Question

if roots of equation ax2+bx+c=0 is m and n the find the equation of roots m+1/n and n+1/m​

Answer 1

Answer:

Step-by-step explanation:

First thing you have to know that m+n = -b/a and mn = c/a

in the new equation x2+ex+f=0 we know that (m+1/n)(n+1/m​) = f

(mn+m+n+1)/mn = f

f = (c-b+a)/c

Also (m+1/n)+(n+1/m​) = -e

(m^2+n^2+m+n)/mn = -e

((m+n)^2+m+n)/mn-2=-e

((b^2-ab)/ac)-2=-e

So new equation will be x^2+((b^2-ab-2ac)/ac)x+((c-b+a)/c) = 0

or cx^2+((b^2-ab-2ac)/a)x+(c-b+a) = 0