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

x 

= 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

Equations, At a bakery the cost of 30 experts is 45$. Write an equation tha...

At a bakery the cost of 30 experts is 45$. Write an equation that shows the cost of 45 cookies

Proportions, bananas are on sale for 3 pounds for $2. At that price how man...

bananas are on sale for 3 pounds for $2. At that price how many pounds can you buy for $22

Method of cylinders or method of shells, Method of cylinders or method of s...

Method of cylinders or method of shells The formula for the area in all of the cases will be,                                                        A = 2 ∏ ( radius ) (heig

What is negative exponents explain, What is Negative Exponents explain? ...

What is Negative Exponents explain? Here's a problem which results in a negative exponent: 3 4 /3 7 = 3 (4-7) = 3 -3 A negative exponent means the same thing as making

Which of the following could not be the translation, If the expression 9y -...

If the expression 9y - 5 represents a certain number, which of the following could NOT be the translation? a. five less than nine times y b. five less than the sum of 9 and y c

Assigment, Q1: Find three positive numbers whose sum is 54 and whose produc...

Q1: Find three positive numbers whose sum is 54 and whose product is as large as possible.

Explain graphing equations with a negative slope, Explain Graphing Equation...

Explain Graphing Equations with a Negative Slope? If the slope is a negative fraction, place the negative sign on either the numerator or the denominator. Example graph y = -2/

I Need Help, If 3200 sweets cost 30 US Dollars how much will 13,500 sweets ...

If 3200 sweets cost 30 US Dollars how much will 13,500 sweets cost ?

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