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

x

=

and x

=

This is derived as follows. We have

         ax² + bx + c       = 0

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

On dividing equation (1) by a, we have x2 +

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

x2 +

 

 

Posted Date: 9/13/2012 4:01:22 AM | Location : United States

Ask an Expert

Related Discussions:- Solving a quadratic equation, Assignment Help, Ask Question on Solving a quadratic equation, Get Answer, Expert's Help, Solving a quadratic equation Discussions

Write discussion on Solving a quadratic equation
Your posts are moderated

Write your message here..

Related Questions

Linear equation, The sum of the digit number is 7. If the digits are revers... The sum of the digit number is 7. If the digits are reversed , the number formed is less than the original number. find the number

Sales tax and discount, Help me in my math! Help me in my math!

Proportions, if oranges cost $2.40 a dozen, how much do 2 oranges cost? if oranges cost $2.40 a dozen, how much do 2 oranges cost?

Parametric equations of parabola., how the parametric equations of parabola... how the parametric equations of parabola are derived?and what is the condition for the parabola whose equation is in the form of general equation of the two intersecting lines?

Basic operations on fractions, A simple example of fraction would be ... A simple example of fraction would be a rational number of the form p/q, where q ≠ 0. In fractions also we come across different types of them. The two fractions

How are Indian customers visiting Shoppers’ Stop any differe, How are India... How are Indian customers visiting Shoppers’ Stop any different from customers of developed western countries?

Relative frequency definition, Relative Frequency  This type of probab... Relative Frequency  This type of probability requires us to make some qualifications. We define probability of event A, occurring as the proportion of times A occurs, if we re

Area related to circle, If ABCD isaa square of side 6 cm find area of shad... If ABCD isaa square of side 6 cm find area of shaded region

Rounding, how do you round to the nearest dollars? how do you round to the nearest dollars?

Number and operations, 1a.if the williams spend $385 a month on food what i... 1a.if the williams spend $385 a month on food what is their monthly income