**Important Concepts and Formulas**

1. An equation of the form

*ax*= 0, where a, b, c are real numbers and a ≠ 0 is called a quadratic equation.^{2}+ bx + c
2. A real number Î± is said to be a root of the quadratic
equation

*ax*= 0, if^{2}+ bx + c*a**Î±*^{2}*+ b**Î±**+ c*= 0. The zeroes of the quadratic polynomial*ax*and the roots of the quadratic equation^{2}+ bx + c*ax*= 0 are the same.^{2}+ bx + c
3. If we can factorize

*ax*, a ≠ 0, into product of two linear factors, then the roots of the quadratic equation^{2}+ bx + c*ax*= 0 can be found by equating each factor to zero. For example, if (x + Î±) and (x + Î²) are the factors of quadratic equation^{2}+ bx + c*ax*= 0, then the roots are x = - Î± and x = - Î².^{2}+ bx + c
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 a

^{2}+ 2ab + b^{2}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:This is also called

**Sreedharacharya formula**.

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6. A quadratic equation

*ax*, a ≠ 0 has^{2}+ bx + c
I.
two
distinct real roots, if

*b*˃ 0,^{2}– 4ac
II.
two
equal roots, if

*b*= 0, and^{2}– 4ac
III.
no
real roots, if

*b*< 0.^{2}– 4ac