16x²-8x+1=0
This a graph question?
2) 2x²-7x+3=0 3)2x²-x-6=0 4)9x²-3x-2=0 5)y²-6y+2=0 6)4x²-20x+25=0 7)4x²-7x-15=0
no its not they are solving quadratic equations all of them
you can solve it by one of the ways used for quadratic equations, like you can try it by using quadratic formula [x=b \pm \sqrt{b ^{2}-4ac}\div2a\]
i dont know how thats the problem
can someone help me with it or what
Thankfully, there is the quadratic formula... it's foolproof... you interested? :D
sure
Well, anytime you're ready, if you have a quadratic equation of the form \[\Large \color{red}ax^2 + \color{blue}bx +\color{green}c = 0\] Where, of course, a is not 0, then the solutions can be quickly obtained using this formula... \[\LARGE x = \frac{-\color{blue}b \pm \sqrt{\color{blue}b^2 - 4\color{red}a\color{green}c}}{2\color{red}a}\] follow this formula (carefully) and you can never go wrong with quadratic equations :D
Let's take the first one as an example... shall we? :)
okay
\[\Large \color{red}{16}x^2 -\color{blue}8x +\color{green}1 = 0 \] In this case, what are your values for a,b, and c?
a=15 b=8 and c=1
Where did you get a = 15? lol Also, note the minus-sign preceding the 8... better rethink your value for b.... With those said, what are the values for a,b, and c? :)
i meant 16 and -8 my fingers and laptop arennt behaving today as you can c
a=16 b=-8 c=1
LOL, it's fine :) So a = 16 b = -8 c = 1 Great :) So, we plug them into the quadratic formula... \[\LARGE x = \frac{-\color{blue}{(-8)}\pm \sqrt{\color{blue}{(-8)^2}- 4\color{red}{(16)}\color{green}{(1)}}}{2\color{red}{(16)}}\] And just solve :)
8+-sqrt 64+64/32
@terenzreignz i dont know exactly how to do this from here
Okay, relax.. deep breaths :D
lol terenz. dont be so dramatic XD
\[\LARGE x = \frac{\color{blue}{(8)}\pm \sqrt{\color{blue}{64}- \color{red}{64}}}{\color{red}{32}}\] Simplify. :)
8/32
simplify? :D
.25
so both answers are .25
Personally, I prefer 1/4, but whatever floats your boat :P
yay lol wanna keep helpin me i get the way you talk lol
I haven't said a word :D Okay, do the second one, I'll watch for errors :)
liar! lol 2x^2-7x+3 a=2 b=-7 c=3 whats the quadratic formula?
\[\LARGE x = \frac{-\color{blue}b \pm \sqrt{\color{blue}b^2 - 4\color{red}a\color{green}c}}{2\color{red}a}\]
okay so -2+-sqrt2^2-4(-7)(3)/2(2)
then simplify to get -2=-sqrt88/4 now what? @terenzreignz
Why -2? I thought b = -7 ?
shooot
okay hold on i got this
7+-sqrt25/4 thats right i know
Very good :) Now simplify.
thats the problem do i actually square it and what do i do with the 7????
i end up with .5 and 3 when i simplify
YOu got \[\Large \frac{7\pm \sqrt{25}}{4}\]
Which really means... \[\Large \frac{7+\sqrt5}{4} \quad and \quad \frac{7-\sqrt5}{4}\]
why square root of 5
whoops... sorry replace that with square root of 25 :)
ok so seven plus 5 and seven -5 divide both by four
Yup :) And those are your answers :D
3 and .5 i was right okay i need to do this one y^2-6y+2=0
so a= 1 b=-6 and c=2
Yes. Go ahead :D
6+5.2915/2=5.14575 6-5.2915/2=.35425
so 5.2 and.4
I wouldn't suggest approximating... leave it in radical form.
meaning
@terenzreignz
Meaning, leave it like this... \[\Large \frac{6\pm \sqrt{36-8}}{2}=\frac{6\pm \sqrt{28}}{2}=\frac{6\pm 2\sqrt7}{2}=3\pm\sqrt7\]
oh ok
I'm sure you can do the others now :)
whered 3 come from
We divided by 2 (to get rid of that denominator)
oh
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