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#1 2005-08-27 11:25:42
- Angela27
- Guest
Determining the zeros...
Hi, I am stuck with finding zeros for this one... >_<;; It may seem easy, but then I am confused with the answers I looked from the back of the book...
x^(2)-8x+5
The answer is 4 + 11^(1/2) and 4 - 11^(1/2)
May I please have help step by step on this one? 
~Angela
#2 2005-08-27 11:35:02
- ahgua
- Member
Offline
Re: Determining the zeros...
Use the formula:
x = -b ± √(b² - 4 ac)
--------------------- for ax² + bx + c
2a
a = 1, b = -8 and c = 5
x = 8 ± √(8² - 4 x 1 x 5)
-------------------------
2(1)
x = 8 ± √(4 x 11)
-----------------
2
x = 8 ± 2 √(11)
---------------
2
x = 4 ± √(11)
∴ x = 4 + √(11) or 4 - √(11)
= 4 + 11^½ or 4 - 11^½
Last edited by ahgua (2005-08-27 11:45:21)
Life is a passing dream, but the death that follows is eternal...
#3 2005-08-27 11:51:10
- Angela
- Guest
Re: Determining the zeros...
I'm sorry, but what formula was that? 
I'm not supposed to be knowing the answers before doing the problem... I am wondering how to determine the zeros by starting with the function itself; x^(2) - 8x + 5... Apparently my math skills are not top-notch... Thanks you so much, though...
#4 2005-08-27 11:52:26
- Angela
- Guest
Re: Determining the zeros...
Wow, lol, okay, never mind...
ahgua wrote:
Use the formula:
x = -b ± √(b² - 4 ac)
--------------------- for ax² + bx + c
2a
a = 1, b = -8 and c = 5
x = 8 ± √(8² - 4 x 1 x 5)
-------------------------
2(1)
x = 8 ± √(4 x 11)
-----------------
2
x = 8 ± 2 √(11)
---------------
2
x = 4 ± √(11)
∴ x = 4 + √(11) or 4 - √(11)
= 4 + 11^½ or 4 - 11^½
#6 2005-08-27 12:31:03
- kylekatarn
- Power Member
Offline
Re: Determining the zeros...
I think there is a simple way to do this
you can check if the polinomial can be reduced to the form (x-a)(x-b)
your have: P(x)=x²-8x+5
lets find the reduced form
(x-a)(x-b)=x²-8x+5
x²-(a+b)x+ab=x²-8x+5
-(a+b)x+ab=-8x+5
now solve the system
a+b=8
ab=5
wich gives us two (a;b) pairs. One one of them is a solution of P(x)=0. By substituition we can find the rigth one.
I find this method very fast and easy but this isn't always that simple. Some quadratics can't be reduced to the (x-a)(x-b) form.
Just use the quadratic formula solver because it works on all cases. I posted this just for fun:)
#7 2005-08-27 12:45:20
- Angela
- Guest
Re: Determining the zeros...
At least I'm learning more... My math skills are pretty stiff... Thanks.
#9 2005-08-27 13:54:31
- ahgua
- Member
Offline
Re: Determining the zeros...
Another way is by the "completing the square".
x² - 8x + 5 = 0
x² - 8x = -5
x² - 8x + 4² = -5 + 4² [When LHS = x² - ax, adding (a/2)² to both sides enables it to be factorise to (x - b)² form]
(x - 4)² = 11
x - 4 = ± √11
x = 4 ± √11
Life is a passing dream, but the death that follows is eternal...
#10 2005-08-30 07:44:11
- John E. Franklin
- Guest
Re: Determining the zeros...
Or another way is to memorize that the center and bottom of an upward facing parabola is at location x=4 because it is one half and negative of the minus eight x. Then substitute 4 for x and determine how far below the x-axis the bottom of the parabola is. Hence y=16-32+5 or negative eleven. Then since the parabola is normal width of one (one x squared term), then take the square root of the eleven height and get the width in either direction on the x-axis. So the parabola crosses the x-axis at about 0.683 and 7.317. If the parabola's x squared term was two, then the parabola would probably be skinnier since y gets twice as big. So in that case, you'd probably take the eleven(distance bottom of parabola is from x-axis) in this example and divide it by two before square rooting it. I just made this all up, so enjoy it.