Answer:
m = (a - b) / (a + b)
Explanation:
Quadratic equations with opposite roots are of the form x^2 - c = 0 where c is some constant. The ' b' of ax^2 + bx + c = 0 is 0.
(x^2 - bx) (ax - c) = (m - 1)(m + 1)
Cross multiplying we have
(x^2 - bx)(m + 1) = (ax - c)(m - 1)
mx^2 + x^2 - mbx - bx = max - ax - mc + c
mx^2 + x^2 - mbx - bx - max + ax - mc + c = 0
(m + 1)x^2 + ( -mb - b - ma + a)x - mc + c = 0
The coefficient of x = 0 so
-mb - b - ma + a = 0
m(-b - a) = b - a
m = (b - a) / (-b-a)
m = -(b - a) / b + a
m = (a - b) / (a + b) (answer).