Maths Class 10 Chapter 4: Quadratic Equations

Maths Class 10 Chapter 4: Quadratic Equations

Important Concepts and Formulas

1.      An equation of the form ax2 + bx + c = 0, where a, b, c are real numbers and a 0 is called a quadratic equation.

2.      A real number Î± is said to be a root of the quadratic equation ax2 + bx + c = 0, if aÎ±2 + bÎ± + c = 0. The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the quadratic equation ax2 + bx + c = 0 are the same.

3.      If we can factorize ax2 + bx + c, a 0, into product of two linear factors, then the roots of the quadratic equation ax2 + bx + c = 0 can be found by equating each factor to zero. For example, if (x + Î±) and (x + Î²) are the factors of quadratic equation ax2 + bx + c = 0, then the roots  are x = - Î± and x = - Î².

4.      A quadratic equation can also be solved by the method of completing the square. For example, we can make the quadratic equation in the form a2 + 2ab + b2 and write it as (a + b)2.

5.      We can also find the roots of the quadratic equation using the quadratic formula which is given by:

, provided that b2 – 4ac 0.

This is also called Sreedharacharya formula.