matematika kuadrat

8/11/2019 matematika kuadrat

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BY :

ALTA DWI DINIENGGA B. (04)

ARWIN DAHRIL N. (06)

AYU WIJI A. (07)EKA PUTRI Y. (11)

RIZKY BADILLAH N. (23)

YOGA ALGHAZALI A. (29)


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actor

Factors are the numbers you multiply together to get

another number:

Example: 3 and 4 are factors of 12, because 3x4=12.

Also 2x6=12 so 2 and 6 are also factors of 12, and

1x12=12 so 1 and 12 are factors of 12 as well.

So ALL the possible factors of 12 are 1,2,3,4,6 and 12.


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Example :

2x2 + 8x + 6 = 0 From the result, we know that

(2x + 6 ) ( x + 1 ) = 0 although the way is different, but

2x + 6 = 0, x + 1 = 0 the result is same . . . . . . .

2x = - 6 x = -1 x = -3 , x = -1

x = -3

x = -3 , x = -1

Or

(2 x + 6 ) (2 x + 2 ) = 0( x + 3 ) ( 2x + 2 ) = 0

x + 3 = 0 2x + 2 = 0

x = - 3 2x = -2

x = -1


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ExampleSimplify quadratic factor in the bellowX23x + 2 = 0

Answer :Quadratic factorx23x + 2 = 0

(x - 2)(x1)=0

End up ,x 2 = 0 ; x - 1 = 0x = 2 x = 1


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Solv ing Quadratic

Equat ions

Unfortunately, most quadratics don't comeneatly squared like this. For your averageeveryday quadratic, you first have to use thetechnique of "completing the square" to

rearrange the quadratic into the neat"(squared part) equals (a number)" formatdemonstrated above.

Example :

Find the x-intercepts of y= 4x22x5.


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This is the original problem. 4x22x5 = 0

Move the loose number over to the other side. 4x22x= 5

Divide through by whatever is multiplied on

the squared term.Take half of the coefficient (don't forget thesign!) of the x-term, and square it. Add thissquare to both sides of the equation.

Convert the left-hand side to squared form,and simplify the right-hand side. (This is

where you use that sign that you kept track ofearlier. You plug it into the middle of theparenthetical part.)

Square-root both sides, remembering the ""on the right-hand side. Simplify as necessary.

Solve for "x=".

Remember that the "" means that you havetwo values for x.


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Solve x2+ 6x7 = 0 by completing the square.

Solution :

This is the original equation.

x2+ 6x7 = 0

Move the loose number over to the other side.

x2+ 6x = 7

Convert the left-hand side to squared form. Simplify the right-handside.

(x+ 3)2= 16

Square-root both sides. Remember to do "" on the right-hand side.

x+ 3 = 4

Solve for "x =". Remember that the "" gives you two solutions.Simplify as necessary.

x= 3 4

x1 = 3 + 4 x2 = -3- 4

= 1 = -7


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1. Consider the general quadratic equation

with a0

2. Start by dividing coefficient of

x2 = ax = b

constant = c

ax2 + bx + c = 0


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3. Input formula

4. Remark.The plus-minus sign states

that you have two numbers.x1=

x2=


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Use the Quadratic Formula to solve

Solution :

a = 2, b = -3, c =

x

1

=

3 5

x

2

=

3 5

4 4


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