Solving a quadratic equation, Mathematics

Assignment Help:

In polynomials you have seen expressions of the form x2 + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we call it an equation. The equations of the second degree in a single variable "x" or "y" are generally referred to as quadratic equations and the most general form of it is

ax2 + bx + c = 0. The roots or solution for the quadratic equation can be obtained by substituting different values for x and selecting that value for which the value of the equation is zero. The methods which we have seen in factorization of polynomials are also applicable to obtain the roots of a quadratic equation. However, in this part we look at a specific method which is only applicable to solve quadratic equations.

According to this method the roots of a quadratic equation ax2 + bx + c = 0 are

= 2436_quadratic equation1.png and x = 1422_quadratic equation.png

This is derived as follows. We have

         ax2 + bx + c       = 0

         ax2 + bx             = - c                                         ........(1)

On dividing equation (1) by a, we have x2 1418_quadratic equation2.png

In order to make the LHS a perfect square, we add to   2073_quadratic equation3.png  to the LHS and since the equality is to be preserved we do so for the other side also. Hence we obtain

x2 +

2304_quadratic equation4.png



 

2076_quadratic equation5.png 


Related Discussions:- Solving a quadratic equation

Integration, ((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

((1/x^1/2-(x-1)^1/2)+(1/(5-3(x-1)^2)^1/2)

How many miles will he jog in 30 minutes, Mike can jog 6.5 miles per hour. ...

Mike can jog 6.5 miles per hour. At this rate, how many miles will he jog in 30 minutes? Thirty minutes is half an hour. Thus, divide the number of miles Mike can jog in one ho

Draw a graph model with the adjacency matrix, QUESTION (a) Draw a graph...

QUESTION (a) Draw a graph model with the following adjacency matrix.                         (b) The diagram below shows different cities labelled a to g and z. Also sh

form a pythagorean triple, A Pythagorean triple is a set of positive integ...

A Pythagorean triple is a set of positive integers (a,b,c) like  a2 + b2 = c2.  Write a function "ispythag" that will receive 3 positive integers (a, b, c in that order) and will r

Facts regarding linear equations, To solve out linear equations we will mak...

To solve out linear equations we will make heavy use of the following facts. 1. If a = b then a + c = b + c for any c.  All it is saying that we can add number, c, to both sides

Derivatives of inverse trig function, Derivatives of Inverse Trig Functions...

Derivatives of Inverse Trig Functions : Now, we will look at the derivatives of the inverse trig functions. To derive the derivatives of inverse trig functions we'll required t

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd