Quadratic Equations Class 10 Notes Maths Chapter 4


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.

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