Easy Way To Quadratic Functions

Solving Quadratic Equations

Let's have a look at how we solve a quadratic equation:

x²-3x+2=0

The easiest way to solve them is to follow certain steps:

Step 1

Find two numbers where when they are multiplied together equal the firstnumber (a=1) multiplied by the third number (c=2). These two numbers when addedto each other must also equal the second number (b=-3).

In the above example, the solution is -2 and -1.
We can see that when added together the result is -3 and that when multiplied together, the result is 2

Step 2

Rewrite the original equation splitting the middle part into two using thenumbers which you found in step 1.

x²-x-2x+2=0

Step 3

Start to factorise both halves of the equation:

x(x-1)-2(x-1)=0

At this point you will know if you are going along the correct track if thefirst bracket is the same as the second bracket.

Step 4

Collect everything before each bracket and put it into one bracket andmultiply this bracket by that which is inside the identical brackets:

(x-1)(x-2)=0

Step 5

In order for the left side of the equation to be equal to 0, one of the twobrackets must equal 0. So either:

a.
x-1=0
x=1

b
x-2=0
x=2

Step 6

Check these answers:

1²-(3*1)+2=0
1-3+2=0
0=0

2²-(3*2)+2=0
4-6+2=0
0=0

Therefore the possible solutions for the above equation are confirmed to be 1 and 2

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April 19th, 2008 A Real Version for the Square root of -1 The i above was conceived from the first letter of Imaginary, because the number representing the square root of -1 doesn’t exist on the real number line. Pythagorus and other great Mathematicians were dumbfounded by the meaning of i, yet in todays higher level Maths, i is now taken for granted. However, it’s true meaning seems to have been bypassed as our interpretation of it still allows history to dominate our think

Test

Test April 19th, 2008 A Real Version for the Square root of -1 i above was conceived from the first letter of Imaginary, because the number representing the square root of -1 doesn’t exist on the real number line. Pythagorus and other great Mathematicians were dumbfounded by the meaning of i, yet in todays higher level Maths, i is now taken for granted. However, it’s true meaning seems to have been bypassed as our interpretation of it still allows history to dominate our thinking basis

Test2

Test2 April 19th, 2008 A Real Version for the Square root of -1 i above was conceived from the first letter of Imaginary, because the number representing the square root of -1 doesn’t exist on the real number line. Pythagorus and other great Mathematicians were dumbfounded by the meaning of i, yet in todays higher level Maths, i is now taken for granted. However, it’s true meaning seems to have been bypassed as our interpretation of it still allows history to dominate our thinking basi

Test3

Test3 April 19th, 2008 A Real Version for the Square root of -1 i above was conceived from the first letter of Imaginary, because the number representing the square root of -1 doesn’t exist on the real number line. Pythagorus and other great Mathematicians were dumbfounded by the meaning of i, yet in todays higher level Maths, i is now taken for granted. However, it’s true meaning seems to have been bypassed as our interpretation of it still allows history to dominate our thinking basi