##### CHAPTER AT A GLANCE

**1. Quadratic Equation**

Standard from of the quadratic equation in the variable x is an equation of the form ax2+bx+c= 0, where a, b, c are real numbers, a not= 0.

Any equation of the form P(x)= 0, where P(x) is a polynomial of degree 2, is a quadratic equation.

**2. Zero(es)/Root(s) of Quadratic Equation**

A real number a is said to be a root of the quadratic equation ax2 +bx+ c = 0, a not= 0 ifa a2 + ba + c = 0.

We can say that x = a, is a solution of the quadratic equation or that a satisfies the quadratic equation.

The zeroes of the quadratic polynomial ax2 + bx + c and the roots of the equation ax2 + bx + c = 0 are same.

A quadratic equation has at most two roots/zeroes.

**3. Relation between Zeroes and Co-efficient of a Quadratic Equation**

**4. Methods of Solving Quadratic Equation**

Following are the methods which are used to solve quadratic equations:**(i)** Factorisation.**(ii)** Completing the square.**(iii)** By using quadratic formula

**5. Methods of Factorisation**

In this method we find the roots of a quadratic equation (ax2 +bx+ c = 0) by factorising LHS it into two linear factors and equating each factor to zero:

**6. Method of Completing the Square**

This is the method of converting L.H.S. of a quadratic equation which is not a perfect square into the sum or difference of a perfect square and a constant by adding and subtracting the suitable constant terms.

**7. Quadratic Formula**

Consider a quadratic equation: ax2+bx+c = 0.

If b2-4ac => 0,then the roots of the above equation are given by:

**8. Nature of Roots**

For quadratic equation ax2+bx+c= 0

(a not=0),value of (b2-4ac) is called discriminant of the equation and denoted as D.

:. D=b2-4ac

Discriminant is very important in finding nature of the roots.

**(i)** If D = 0, then roots are real and equal.**(ii)** If D > 0, then roots are real and unequal**(iii)** If D < 0, then roots are not real.

**Related Articles:**

- Class 10 Notes
- CBSE Class 10 Maths Notes
- NCERT Solutions for class 10th Maths Chapter 4 Quadratic Equations