QUADRATIC EQUATIONS

Class 10 Maths Formulas

CHAPTER 4 QUADRATIC EQUATIONS
1.	Standard form of a Quadratic Equation is ax² + bx + c = 0, a ≠ 0
2.	Examples of Quadratic Equations: x² − 6x + 4 = 0 2x² − 7x = 0
3.	Examples of equations which are not quadratic: x + 3/x = x² x² + 2√x − 3 = 0
4.	A real number α is a root of the quadratic equation ax² + bx + c = 0 if aα² + bα + c = 0 Then x = α is a solution.
5.	Zeros of the quadratic polynomial ax² + bx + c are the same as the roots of the quadratic equation ax² + bx + c = 0
6.	Factorisation Method: If ax² + bx + c = 0 can be factorised into two linear factors, then equate each factor to 0 to find the roots.
7.	Formula Method: The real roots of ax² + bx + c = 0 are given by: (−b ± √(b² − 4ac)) / 2a where b² − 4ac ≥ 0
8.	Nature of the roots depends on the discriminant D = b² − 4ac
9.	For the quadratic equation ax² + bx + c = 0: (i) Two distinct real roots if b² − 4ac > 0 (ii) Two real and equal roots if b² − 4ac = 0 (iii) No real roots if b² − 4ac < 0