Maths Formulas Chapter-04 | Quadratic Equations

Quadratic equation Chapter 4 Class 10

Basic concepts on Quadratic Equation class 10, chapter 4,  Nature of roots, Discriminant, Quadratic Formula, method of completing the square. Complete explanation of quadratic equations

QUADRATIC EQUATION :- 

An equation whose degree is 2 is called a quadratic equation.

General Quadratic Equation is  ax² + bx + c = 0 

Here "a" is the coefficient of x² , 

"b" is the coefficient of x and 

"c" is the constant term. 

Difference between the quadratic equations and quadratic polynomials.

Quadratic equations are very similar to the quadratic polynomials. But they are different from each other because of the following reasons.

Quadratic Equations	Quadratic Polynomials
General Quadratic Equations is    ax2 + bx + c = 0	General Quadratic Polynomial is  P(x) = ax2 + bx + c
Solutions of quadratic equations are called its roots.	Solutions of quadratic polynomials are called its zeroes.

Methods of Solving Quadratic Equations

There are mainly three methods of solving Quadratic equations

1) Factor Method

2) By Quadratic Formula

3) My the method of Completing the Square.

ROOTS:-

Solutions of the quadratic equations are called its roots. A quadratic equation have two roots.

 RELATION BETWEEN ROOTS AND COEFFICIENTS:-

Quadratic Equation From The Roots:-

x² – (Sum of roots)x + Product of roots = 0

x² – Sx + P = 0

Nature Of The Roots Of The Quadratic Equation:-

General quadratic equation is 

 ax² + bx + c = 0

Discriminant of quadratic equation is denoted by D and is given by

D = b² - 4ac

If D > 0  then  roots are real and unequal or distinct or different)

If D = 0  then  roots are  real and equal

If D < 0  then  roots are  not real

If D ≥ 0  then  roots are real

Quadratic Formula For Solving The Quadratic Equations:-

Method of completing the square:-

Write the given quadratic equation

ax² + bx + c = 0

Make the coefficient of x² unity

Bring the constant term to the right hand side.

Completing the square 

Taking the square root on both side

Find the value of x

Example

Find the roots of  5x2 - 6x - 2 = 0 by the method of completing the square Given equation is   5x2 - 6x - 2 = 0 D = b2 - 4ac  ⇒ D = (-6)2  - 4 x 5 x -2 = 36+40 = 76 > 0 ⇒ Roots are real and distinct ⇒ Roots of Q. E. are exists Now we apply method of completing the square as follows Step (1) Make the coefficient of x2 unity ( divide the equation by 5) Step (2) Bring the constant term to the RHS Step (3)     Step (4)  Completing the square and find the square root

Method of solving the Q. E. by using quadratic formula

Find the roots of 5x2 - 6x - 2 = 0 by the Quadratic Formula Given equation is 5x2 - 6x - 2 = 0 D = b2 - 4ac ⇒ D = (-6)2  - 4 x 5 x -2 = 36 + 40 = 76 > 0 ⇒ Roots are real and distinct ⇒ Roots of Q. E. are exists Now we apply the quadratic formula

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Maths Assignment Class 10

Chapter 4

Quadratic Equations

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