## Vivek Tiwari

teacher | Physics

### Description

QUADRATIC EQUATION - INTRODUCTION , SOLUTION OF QUADRATIC EQUATION & RELATION BETWEEN ROOTS & CO-EFFICIENTS

INTRODUCTION

The algebraic expression of the form ax2 + bx + c, a  0 is called a quadratic expression, because the highest order term

in it is of second degree. Quadratic equation means, ax2 + bx + c = 0. In general whenever one says zeroes of the

expression ax2+bx + c, it implies roots of the equation ax2 + bx + c = 0, unless specified otherwise. A quadratic

equation has exactly two roots which may be real (equal or unequal) or imaginary.

SOLUTION OF QUADRATIC EQUATION & RELATION BETWEEN ROOTS & CO-EFFICIENTS

a.

The general form of quadratic equation is ax2 + bx + c = 0, a != 0.

The roots can be found in following manner :

This expression can be directly used to find the two roots of a quadratic equation

b.

The expression

is called the discriminant of the quadratic equation.

c.

if

1.

2.

3.

d.A quadratic equation whose roots are

Example :

if are  the roots of a quadratic equation , then the equation whose roots are

Solution :

since are  the roots of a quadratic equation

so

Putting

2 and 2 are the roots.

The required equation is

Logarithm : Principal Propertise of Logarithm

Principal Propertise of Logarithm

if m, n are orbitrary positive real numbers where  a > 0 ; a !=1

1.

Proof :

let

Now

so

2.

prof:

so

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