Question: how to solve quadratic equations with common roots?
Answer: Condition for one common root: ⇒ (c1a2 - c2a1)^2 = (b1c2 - b2c1)(a1b2 - a2b1), which is the required condition for one root to be common of two quadratic equations. Note: (i) We can find the common root by making the same coefficient of x^2 of the given equations and then subtracting the two equations.