Nature Of Roots
Chapter Name : Quadratic Equations |
Sub Topic Code : 104_10_04_05_01 |
Topic Name : Nature Of Roots |
|
Sub Topic Name : Nature Of Roots |
|
Introduction
Quadratics Equations are a useful tool to solve problems in two degrees and their factors help us to solve them for solutions of various problems directly associated with real life. Nature of roots of the equation helps us to know whether the graph of the equation will cut real axis of not.
Pre-Requisites:
Idea about Quadratic Equations, roots of a quadratic equation.
Activity:
Is it possible to design a rectangular park of perimeter 80 m and area 400 m2? If so, find its length and breadth.
Real Life Question:
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the differences of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it possible to do so?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Discriminant | b2 – 4ac determines whether the quadratic equation ax2 + bx + c=0 has real roots or not, this (b2 – 4ac) is called the discriminant of the quadratic equation ax2 + bx + c=0. |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Graphs | Plot the quadratic equation 2x2 – 6x + 3 = 0 on the x-y plane and see if the curve cuts x or y axis or not. If it does, then the roots of the quadratic equation are real. |
Real life uses :
NASA relies on aircraft that fly in a parabolic arc in which to train astronauts. The arc is made using the quadratic equation. Financial Analysts use discriminants to analyze and predict a company’s future earnings.
Places to visit :
Math Lab.
Practical examples around us
| Examples | Explainations |
|---|---|
| 1. Newton’s second law of motion. | S=ut+1/2 at2, this law of motion is infact a quadratic equation in time. |
What you learn in Theory:
What is the discriminant of a quadratic equation and what are real, imaginary and distinct roots.
What you learn in Practice:
How to find the discriminant of a quadratic equation and therefore predict whether the equation has real or imaginary roots.