Dear student,

The equation is given as :-

x^2 + bx + c = 0

Now, it is given that one root of the equation is n times the other root. So, let one of the root be k.

So, the other root will become nk.

Now sum of root = - coefficient of x / coefficient of x^2

Product of roots is = constant term / (coefficient of x^2)

Now,

Sum of root = nk+k = k(1+n) = -b /1

And product of root = (nk)k = nk^2 = c /1

From equation 1st, we have :-

k = -b/(1+n)

Substituting the value of k in equation 2nd we get :-

{(1+n)^2} / n = (b^2) / c

So, we got our final condition, if one of the root is n times the other.