Q. a(b - c)x^2 + b(c - a)x + c(a - b) = 0 has equal roots then b = ?
Ans: Condition that a quadratic equation ax² + bx + c = 0 has equal roots is:
Its discriminant, b² - 4ac = 0
Applying this, b²(a - c)² - 4ac(a - b)(c - a) = 0
Expanding and simplifying, a²b² + b²c² + 4c²a² + 2ab²c - 4abc² - 4a²bc = 0
(ab + bc - 2ac)² = 0
ab + bc - 2ac = 0
b(a + c) = 2ac
Solving b = 2ac/(a + c)