Fellow mathematicians,
I need some help with quadratic eqations. The main part of quadratics which i need help on from my mathematics book is factorising quadratics
Regarding the factorising of quadratics there are two types- the one which states that a=1 and the one which states a is not 1. I'm having problems with the theorem which states a is not equal to 1.
I have listed some examples. I was wondering could you go through them coherently.
1. 4x^2 + 3x - 1
2. 3x^2 + 2
3. 3x^2 +5x - 2
4. x^2 - 6x + 9 = 16
5.(x+3)^2 - 3 = 13
Also most importantly when i've been doing a=1 i've been working with three digits in total, but strangly in question 4 there is 4 digits unlike question 1. Could someone please help.
Many thanks. All comments are very much appreciated.
Quadratic Equations?
2008-07-05 5:54 pm
回答 (5)
2008-07-05 5:58 pm
✔ 最佳答案
-b + or - square root of b^2 -4ac
2008-07-06 1:08 am
4x^2 + 3 x -1
here a = 4, b = 3 and c= - 1
a* c = 4* (-1) = -4
Break up the product a*c into two factors whose sum is b i.e. 3 in this case. Doing this we get
4 and -1
Next break up the expression splitting the middle term into two terms namely factors of a*c, Doing this we get the expression as
4x^2 + 4 x -x-1
or 4x(x+1)-(x+1)
or (x+1) (4x-1) as the required factors
here a = 4, b = 3 and c= - 1
a* c = 4* (-1) = -4
Break up the product a*c into two factors whose sum is b i.e. 3 in this case. Doing this we get
4 and -1
Next break up the expression splitting the middle term into two terms namely factors of a*c, Doing this we get the expression as
4x^2 + 4 x -x-1
or 4x(x+1)-(x+1)
or (x+1) (4x-1) as the required factors
2008-07-06 1:02 am
4. x^2 - 6x + 9 = 16
Rewrite this as
x^2-6x+9-16=0
x^2-6x-7=0
x^2-7x+x-7=0
x(x-7)+1(x-7)=0
(x-7)(x+1)=0
x=7 and x=-1
Rewrite this as
x^2-6x+9-16=0
x^2-6x-7=0
x^2-7x+x-7=0
x(x-7)+1(x-7)=0
(x-7)(x+1)=0
x=7 and x=-1
2008-07-06 1:01 am
1)
4x^2 + 3x - 1
= 4x^2 + 4x - x - 1
= 4x(x + 1) - 1(x + 1)
= (x + 1)(4x - 1)
2)
3x^2 + 2
= cannot be factored
3)
3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x(x + 2) - 1(x + 2)
= (x + 2)(3x - 1)
= = = = = = = =
4)
x^2 - 6x + 9 = 16
x^2 - 6x + 9 - 16 = 0
x^2 - 6x - 7 = 0
x^2 + x - 7x - 7 = 0
x(x + 1) - 7(x + 1) = 0
(x + 1)(x - 7) = 0
x + 1 = 0
x = -1
x - 7 = 0
x = 7
â´ x = -1 , 7
= = = = = = = =
5)
(x + 3)^2 - 3 = 13
(x + 3)(x + 3) - 3 - 13 = 0
x^2 + 3x + 3x + 9 - 3 - 13 = 0
x^2 + 6x - 7 = 0
x^2 + 7x - x - 7 = 0
x(x + 7) - 1(x + 7) = 0
(x + 7)(x - 1) = 0
x + 7 = 0
x = -7
x - 1 = 0
x = 1
â´ x = -7 , 1
4x^2 + 3x - 1
= 4x^2 + 4x - x - 1
= 4x(x + 1) - 1(x + 1)
= (x + 1)(4x - 1)
2)
3x^2 + 2
= cannot be factored
3)
3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x(x + 2) - 1(x + 2)
= (x + 2)(3x - 1)
= = = = = = = =
4)
x^2 - 6x + 9 = 16
x^2 - 6x + 9 - 16 = 0
x^2 - 6x - 7 = 0
x^2 + x - 7x - 7 = 0
x(x + 1) - 7(x + 1) = 0
(x + 1)(x - 7) = 0
x + 1 = 0
x = -1
x - 7 = 0
x = 7
â´ x = -1 , 7
= = = = = = = =
5)
(x + 3)^2 - 3 = 13
(x + 3)(x + 3) - 3 - 13 = 0
x^2 + 3x + 3x + 9 - 3 - 13 = 0
x^2 + 6x - 7 = 0
x^2 + 7x - x - 7 = 0
x(x + 7) - 1(x + 7) = 0
(x + 7)(x - 1) = 0
x + 7 = 0
x = -7
x - 1 = 0
x = 1
â´ x = -7 , 1
2008-07-06 1:00 am
1-3 are not equations.
********************************
4: (x-3)^2 = 16
x-3 = +/- 4
x = 3 +/- 4
x = 3+4 or 3-4
x = 7 or -1
*****************************
5: (x+3)^2 = 16
x+3 = +/- 4
x = -3 +/- 4
-3+4 = 1
-3 - 4 = -7
x = 1 or -7
********************************
4: (x-3)^2 = 16
x-3 = +/- 4
x = 3 +/- 4
x = 3+4 or 3-4
x = 7 or -1
*****************************
5: (x+3)^2 = 16
x+3 = +/- 4
x = -3 +/- 4
-3+4 = 1
-3 - 4 = -7
x = 1 or -7
收錄日期: 2021-05-01 10:47:04
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