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Please help very confused

LCW

New member
Joined
Dec 7, 2009
Messages
2
Well i am so confused i have asked my dad for help but he could nto show me i looked all over the web and i have submitted answers i thought were right online numerous times and keep getting them wrong could some kind person just do these 3 simple problems for me ans show work so i can see what i was doing wrong i have like a page for each problem of me repeatedly trying them but i know i am just missing 1 small step. the ^ means to the power of like ^2 to the power of 2 just like on a calculator

1.)The quadratic equation

X^2-2X-1=0
has two real solutions. The smaller one is ?


2.)
1 pt) Solve the equation x^2-6x+8=0

The solutions are X^1= _____ and X^2____

3.)Find all real solutions of the equation x^2-125=0

x^1=____ and x^2=11.18.03 ( i figured that one out)



if you could help that would be really really awesome cuz these are bothering me
 

chrisr

Full Member
Joined
Nov 29, 2009
Messages
355
Sometimes it's easy to write a quadratic using factors and sometimes it's too difficult.

x[sup:25jc96ij]2[/sup:25jc96ij]-2x-1 is a case where you must use the alternative, the quadratic formula.
ax[sup:25jc96ij]2[/sup:25jc96ij]+bx+c=0 for x= {-b+sqrt(b[sup:25jc96ij]2[/sup:25jc96ij]-4ac)}/2a and x = {-b-sqrt(b[sup:25jc96ij]2[/sup:25jc96ij]-4ac)}/2a.

The smaller one will be the one with the - after -b.

You can do the same with the 2nd one, but that one is easy to write factors for.
Two numbers multiply to give 8 and add to give -6.
They are -4 and -2,

so x[sup:25jc96ij]2[/sup:25jc96ij]-6x+8 = (x-4)(x-2).

If this is zero, what could x be ? since zero multiplied by anything is zero.
The two values of x that cause that to be zero are x[sub:25jc96ij]1[/sub:25jc96ij] and x[sub:25jc96ij]2[/sub:25jc96ij].

For the 3rd, you can rewrite that as x[sup:25jc96ij]2[/sup:25jc96ij] = 125.
Now 3(3) = 9, but -3(-3) is also 9, so what is the value of x[sub:25jc96ij]1[/sub:25jc96ij]?
 
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