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

Calculus level 2, the first question should be done using the website given...

the first question should be done using the website given (www.desmos.com/calculator )and another good example to explain using the graph ( https://www.desmos.com/calculator/ydimzr

Find the value of p and q for which the system of equations, Find the value...

Find the value of p and q for which the system of equations represent coincident lines 2x +3y = 7, (p+q+1)x +(p+2q+2)y = 4(p+q)+1 Ans: a 1  = 2, b 1 = 3, c 1 = 7 a 2  =

Terminology of polynomial, Terminology of polynomial Next we need to ge...

Terminology of polynomial Next we need to get some terminology out of the way. Monomial polynomial A monomial is a polynomial which consists of exactly one term.

Standard hypothesis tests, Standard Hypothesis Tests In principal, we c...

Standard Hypothesis Tests In principal, we can test the significance of any statistic related to any type of probability distribution. Conversely we will be interested in a few

Example to understanidng of multiplication, 6-year-old Rahul wasn't able to...

6-year-old Rahul wasn't able to understand multiplication when it was thrust upon him in school. His mother discussed this problem with some of us. On the basis of suggestions that

Introduction to learning to count, INTRODUCTION : Most of us, when plannin...

INTRODUCTION : Most of us, when planning the first mathematical experience for three-year olds, think in terms of helping them memorise numbers from 1 to 20. We also teach them to

Compute the dot product for the equation, Compute the dot product for each ...

Compute the dot product for each of the subsequent equation  (a) v → = 5i → - 8j → , w → = i → + 2j →  (b) a → = (0, 3, -7) , b → = (2, 3,1) Solution (a) v →

Properties of definite integral, Properties 1.  ∫ b a f ( x ) dx = -∫ ...

Properties 1.  ∫ b a f ( x ) dx = -∫ b a f ( x ) dx .  We can interchange the limits on any definite integral, all that we have to do is tack a minus sign onto the integral

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