Factoring quadratic equation into binomials

Factoring quadratic equation into binomials:
    Remember how we factorized polynomials of the second degree? How do we factorize `x^2 + 7x + 12`?
12 = 1 x 12             1 + 12 = 13
12 = 2 x 6                2 + 6 =8

12 = 3 x 4      3 + 4 = 7

`x^2 + 7x +12` = `x^2 +(3 + 4)x + (3 x 4)`
                               = `(x+3)(x+4)`
There is another way of doing such factoring quadratic binomials. Supppose we want to find the factors of p(x) = `x^2 + 3x -10`. We know that if x - a factor of p(x), then p(a) = 0. In other words, a is a solution of the equation p(x) = 0;m that is, the equation `x^2+3x -10 =0` .
We know how to solve the quadratic equation `x^2 + 3x -10 = 0`. Using the quadratic formula

Factoring Quadratic Binomial Formula:

   The quadratic equation `ax^2 + bx + c = 0` of  factoring  formulae:

                  `x` ` =` ` (-b +-sqrt(b^2 - 4ac))/2`  

In the above problems,

                 x = -3 `+-` ` sqrt(3^2 - 4 .1 . (-10))/2`    =  (-3 `+-` `sqrt(59)` ) / 2 

                                                                             = (-3 `+-` 7)/ 2

                                                                             = 2 or -5

   Thus if we write p(x) = `x^2 + 3x -10 `, then p(2) = 0 and p(-5) = 0, so that by the Factor Theorem x-2 and x-(-5) = x + 5 are factors of p(x). By actual multiplication, we do find

                               (x - 2) (x +5) = `x^2 + 3x -10`

Examples for Factoring Quadratic Binomials:

Example 1:

Factoring the quadratic equation `6x^2-11x+3`into binomials.

Solution:

Given:

    `6x^2-11x+3`

To factor the above quadratic equation, we put the values for a, b, and c into the quadratic formula.

like this:

Calculating these expressions through, we get that

                                                  One root or solution is: 1.500
                                                  and the other root or solution is: 0.333
                                                  These answers have been rounded to 3 digits after the decimal point.

 Therefore, the required binomials are `(x - 1.500)` and `(x - 0.333)` 

Example 2:

Factoring the quadratic equation `x^2 -2x-1 =0` into binomials.

Solution:

To factor the above quadratic equation, we put the values for a, b, and c into the quadratic formula

like this:

Calculating these expressions through, we get that

One root or solution is: 2.414
and the other root or solution is: -0.414
These answers have been rounded to 3 digits after the decimal point.

Therefore the required binomials are `(x - 2.414)`  and `(x + 0.414)` .

Introduction to math answer generator

Introduction to Math Answer Generator:

            The generator in the sense, a author who solves the set of math problems and delivers the answer. Here we consider the generator produces algebra problems with detailed answer. Algebra is the main branch of mathematics use to find out the unknown variables with the help of known variables. In math, Algebra gives the basic ideas to solve the expressions, equations etc. In algebra the answer generator delivers the stepwise solution to problems.

Understanding 6th Grade Math Answers is always challenging for me but thanks to all math help websites to help me out.

Examples for Math Answer Generator:

Ex 1: Simplify the math expression 3(a -4) + 2b - 3(a -b -5) + 4
Sol :   Given the algebraic expression

3(a -4) + 2b - 3(a -b -5) + 4
Multiply factors.

= 3a - 12 + 2b -3a + 3b + 15 + 4
Grouping the terms

= 5b + 7
Ex 2:   Find the distance between the points below
 (1,3) and (7,11).
Sol :  The distance d between points (-1, -3) and (-7, -11) is given by

d = sqrt [(1 - 7) 2 + (3 - 11) 2]
Simplify.

d = sqrt (36 + 64) = 10
Ex 3 : Find the x intercept of the graph of the equation.
                      3x - 5y = 6
Sol :   Given the equation

3x - 5y = 9
To find the x intercept we set y = 0 and solve for x.

3x - 0 = 9
Solve for x.

x = 9 / 3 =3
The x intercept is at the point (3, 0).
Ex 4 : Determine the slope of the line
         8x - 8y = 16
Sol :  Given the line

8x - 8y = 16
Write the above equation in slope intercept form y = mx + b and identify the value of m the slope.

-8y = -8x + 16

y = x - 2
The slope is given by the coefficient of x, which is 1.
         Slope = 1
       
Practice Problems for Math Generator:

1) Find the x intercept of the graph of the equation.
             6x - 8y = 3
Ans : The x intercept is at the point (0.5, 0).

2) Evaluate f (4) - f (3)
            f(x) = 6x + 4
Ans :   6

LEARNING ABOUT DIFFERENCE QUOTIENTS

The Difference Quotient is an important topic of study under Calculus. It is defined as the function difference divided by the point difference.
It is given by the formula :

Delta F(P) / Delta P
= F(P+ Delta P)- F(P) /Delta P
= Delta F (P +Delta P) / Delta P

Where, Delta P is the difference between 2 points.
Difference quotient is also often known as Newton's Quotient.

Students need to learn the difference between Difference Quotient Derivative and as a Divided Difference.

Students can also learn about Higher order Difference quotients like the:

• Second order
• Third order
• Nth order

SOLVING EQUATIONS IN ALGEBRA

Algebra is a branch of Math which deals with study of rules of operations and concepts related to them like variables, equations, expressions etc,. Equations are an important topic of study under algebra.
Equations are values or expressions separated by an ' = ' (equal to) sign. In Algebra, equations consist of variables. Equations are of different types based upon the exponential value to the 'degree' to which they are raised to. They are :

• Linear Equations
• Differential Equations
• Quadratic Equations
• Radical Equations etc,.

Students can learn to solve simpler Linear Equations first. They are called 2 Step equations. They can first learn to Solve 2 step equations. These, as the name suggests, can be solved in 2 simple steps.

• First step would involve grouping of Variables and constants
• Second would be determining the value of the variable.

Students can also learn solving more complex equations like Solve 5x equations are involved. There might be 2 algebraic expressions forming a second or third degree equation to be solved.

convert 1 pound in dollars

Lets work some simple word problem to convert 1 pound in dollars below. We learn t how to convert 1 million to thousands earlier, does any body remember

If you are in United States of America .But you are from England. You get it in 350 pounds. If you are a visitor to England and to go to a nearby shopping center to buy a wine and you get to know the rate of wine is 200 dollars . how many dollars would you give to the shop keeper?

Solution:

Formula for converting pounds to dollar

1 pound 1.51 dollars

Multiplied by 350 for both sides

350 pounds 528.5 dollars

Now you give 350 pounds to shopper.

528.5 - 200 dollars = 328.5 dollars converted into pounds.

They will return to 328.5 dollars.

Answer:

The shopper gives to 328.5 USD.

Will come back again with some more interesting topic friends, until then keep smiling and let me know your comments on this. How about discussing on formula circumference of a circle shortly, do you like this idea?

Formula for conditional probability

I have worked on probability functions many times till date. We also had a conditional probability quiz too? Did you see that? Did you guys work on it?

Here below i have a formula which will help you learn conditional probability.




Get prepared with some sample problems and i will come back with some more questions on this. Guys i came across a site which helped me in unit circle trigonometry try it out.

composite numbers 1-100

Friends do you know composite numbers 1-100 come on, can any body tell me those numbers? I have discussed on various numbers such as prime numbers, whole numbers and i have also briefed you with what is composite numbers.

Guys to learn composite numbers 1-100 we need to know what does composite number mean actually.

Composite numbers:- The numbers which can be divided by more than 1 but number except 1 and the number itself.

Composite numbers 1-100 are as shown below.

4,6,8,9,10,12,14,15,16,18,20,21,22,24,25,26,27,28,30,32,33,34,35,36,38,39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,

62,63,64,65,66,68,69,70,72,74,75,76,77,78,80,81,82,84,85,86,87,88,90,91,92,93,94,95,96,98,99,100.......

One more important information i would like to give you is guys you can use simplifying radical expressions calculator when you simplify radical expressions.