So a quadratic equation which is a polynomial equation of order 2 must have 2 solutions. In quadratic equation ax2 bx c 0 or x b2a2 D4a2 If a 0 minimum value 4ac b24a at x -b2a. One common root if b1c2 b2c1c1a2 c2a1 c1a2 c2a1a1b2 a2b1 Both roots common if a1a2 b1b2 c1c2.
For example the equation given by the equation x² 1 0 there is no real number such that satisfies this equation since both x² is greater than or equal to zero and 1 is greater strict.
When working with real numbers quadratic equations can have. Hence the other root of the required equation is 2 3 Since the surd roots always occur in pairs so another root is 2 3. F x x2 - 1. The discriminant is b2 - 4ac which comes from the quadratic formula and we can use this to find the nature of the roots.