TOPICS

Introduction

Quadratic Equations

A quadratic equation in the variable x is an equation of the form ax² + bx + c = 0, where a, b, c are real numbers, a ≠ 0.

For example, 2x² + x – 300 = 0 is a quadratic equation.

The uncertainty of ‘probably’ etc can be measured numerically by means of ‘probability’ in many cases.

So, x² + 4x – 5 = 0 can be written as (x + 2)² – 9 = 0 by this process of completing the square. This is known as the method of completing the square.

Thus, if b² – 4ac ≥ 0, then the roots of the quadratic equation ax² + bx + c = 0 are given by This formula for finding the roots of a quadratic equation is known as the quadratic formula.

b² – 4ac determines whether the quadratic equation ax² + bx + c = 0 has real roots or not, b² – 4ac is called the discriminant of this quadratic equation.

So, a quadratic equation ax² + bx + c = 0 has

(i) two distinct real roots, if b² – 4ac > 0,

(ii) two equal real roots, if b² – 4ac = 0,

(iii) no real roots, if b² – 4ac < 0.

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