Quadratic Equation

Aug 09, 2022, 16:45 IST

History of Quadratic Equation

He was famous during his lifetime as a mathematician, documented for inventing the tactic of solving equations by intersecting a parabola with a circle. Although his approach at achieving this had earlier been attempted by Menaechmus et al., Khayyám provided a generalization extending it to all or any cubics. additionally he discovered the binomial expansion, and authored criticisms of Euclid's theories of parallels which made their thanks to Europe, where they contributed to the eventual development of non-Euclidean geometry. In 1070 he wrote his greatest work on algebra. In it he classified equations consistent with their degree, and gave rules for solving quadratic equations, which are very almost like those in use today, and a geometrical method for solving cubic equations with real roots. He also wrote on the triangular array of binomial coefficients referred to as Pascal's triangle. In 1077, Omar wrote Sharh ma ashkala min musadarat kitab Uqlidis (Explanations of the Difficulties within the Postulates of Euclid). a crucial a part of the book cares with Euclid's famous parallel postulate, which had also attracted the interest of Thabit ibn Qurra. Al-Haytham had previously attempted a demonstation of the postulate; Omar's attempt was a definite advance. Omar Khayyam also had other notable add geometry, specifically on the idea of proportions.

Table of content for Quadratic Equation

· Introduction

· Roots of quadratic equation

· To find root of quadratic equation

· Nature of roots

· Condition for Common roots

· Quadratic Equation

· Graph of Quadratic Expression

· Greatest and least value of Quadratic Expression

· Sign of Quadratic Expression

Introduction to Quadratic Equation

A quadratic, when equated to zero, becomes a quadratic equation. The values of x satisfying the equation are called the roots of the quadratic equation.

General from: ax² + bx + c = 0

where a, b, c are called coefficients of this equation.

Roots of Quadratic Equation

The values of variables satisfying the given quadratic are called its roots. In other words, x = α may be a root of the quadratic f(x), if f(α) = 0.The real roots of an equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersect the x-axis.

· One of the roots of the quadratic is zero and therefore the other is -b/a if c = 0

· Both the roots are zero if b = c = 0

· The roots are reciprocal to every other if a = c