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

Mode, how to work out mode

how to work out mode

Estimate the probability, The following (artificial) data record the length...

The following (artificial) data record the length of stay (in days) spent on a psychiatric ward for 28 consecutive patients who have been sectioned under the mental health act, cla

Calculate the monthly payment amount of the loan, Consider a student loan o...

Consider a student loan of $12,500 at a fixed APR of 12% for 25 years, 1. What is the monthly payment amount? 2. What is the total payment over the term of the loan? 3. OF

Continuity, give me some examples on continuity

give me some examples on continuity

Hypothesis testing about the difference between two proporti, Hypothesis Te...

Hypothesis Testing About The Difference Between Two Proportions Hypothesis testing about the difference between two proportions is used to test the difference between the propo

Consumer behavior, explain big 5 ppersonality model, suggest thier target m...

explain big 5 ppersonality model, suggest thier target market and one marketing strategiy for each .

The perimeter of a rectangle is 104 inches find out width, The perimeter of...

The perimeter of a rectangle is 104 inches. The width is 6 inches less than 3 times the length. Find out the width of the rectangle. Let l = the length of the rectangle and let

How long will it take the light to blink 405 times, The light on a lighthou...

The light on a lighthouse blinks 45 times a minute. How long will it take the light to blink 405 times? Divide 405 by 45 to get 9 minutes.

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