Which of the following is a solution of x2 + 4x + 6? −2 + i times the square root of 2 2 + i times the square root of 2 −2 + three i times the square root of 2 −2 + three i times the square root of 2

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Which of the following is a solution of x2 + 4x + 6? −2 + i times the square root of 2 2 + i times the square root of 2 −2 + three i times the square root of 2 −2 + three i times the square root of 2

Mathematics
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you have a choice you can use the quadratic formula or you can complete the square you pick
actually there is a third choice, namely to cheat
how do i do that, any of it ?

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Other answers:

do you know the quadratic formula?
i need a refresher.
the solutions to \[ax^2+bx+c=0\] are \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\] in your case \(a=1,b=4,c=6\) but also in your case completing the square is easier
lets solve \[x^2+4x+6=0\] by completing the square ready?
sorry i was working it out xD
ok take your time
so far I got |dw:1438546685018:dw|
\[4^2-4\times 6=-8\]
\[x=\frac{-4\pm\sqrt{-8}}{2}\]
then \[\sqrt{-8}=\sqrt{4\times 2\times (-1)}=\sqrt{4}\sqrt{2}\sqrt{-1}=2\sqrt{2}i\]
giving you \[\frac{-4\pm2\sqrt{2}i}{2}\] divide each term by \(2\) and get \[-2\pm\sqrt{2}i\]
it would have been easier to complete the square there would have been no denominator
is that supposed to be the answer ?
lol yes it is "supposed to be" but in fact they wrote \[-2\pm i\sqrt{2}\]
xD are you able to help me out with more ?
sure
Solve x2 + 4x + 1 = 0. x equals the quantity of 4 plus or minus square root 12 all over 2 x equals negative 4 plus or minus square root 3 x equals negative 2 plus or minus square root 3 x equals the quantity of 4 plus or minus square root 13 all over 2
lets complete the square for this one, unless you want to use the formula again
in fact i will just write down the steps for completing the square without skipping any so you can try one on your own
\[x^2+4x=1=0\] subtract 1 from both sides get \[x^2+4x=-1\]
alright
then half of 4 is 2, and 2 squared is 4 go right to \[(x+2)^2=-1+4\] or \[(x+2)^2=3\]
take the square root of both sides, don't forget the \(\pm\) get \[x+2=\pm\sqrt3\]
subtract 2 from both sides to solve for x, get \[x=-2\pm\sqrt3\] done
looks like option C in your choices
xD I thought I wa supposed to do it lol
Solve 6 over x minus 4 equals 4 over x for x and determine if the solution is extraneous or not. x = -8, extraneous x = -8, non-extraneous x = 8, extraneous x = 8, non-extraneous what about this one xD
this is not a quadratic i guess
\[\frac{x}{x-4}=\frac{4}{x}\] right?
no that is not right \[\frac{6}{x-4}=\frac{4}{x}\] hows that?
the x in the numerator is a 6
as the math teacher say "cross multiply" and get \[6x=4(x-4)\] which is a linear equation can you solve that one?
yea let me try xD
i will wait
x=-8?
yes
would it be extraneous?
how do i tell if its extraneous or non-extraneous?
if it does not make the denominator zero, then it is not extraneous or put another way, if it does make the denominator zero, then it is extraneous
in this case it does not, so it is not extraneous
oh now i get it
\[\frac{6}{x-4}=\frac{4}{x}\] sustitute \(x=-8\) get \[\frac{6}{-8-4}=\frac{4}{-8}\] or \[-2=-2\] a perfectly good solution
well actually \[-\frac{1}{2}=-\frac{1}{2}\] but you get the idea
you up for some more xD? Or you tired out?
go ahead
What is the axis of symmetry for f(x) = 2x2 + 8x + 8? x = −2 x = −4 x = 4 x = 2
oops axis of symmetry of \(y=ax^2+bx+c\) is \[-\frac{b}{2a}\]
in your case \(a=2,b=8\)
let me know when you get \[x=-2\]
what is c?
nothing?
c in your case is 8 but it does not figure in to the axis of symmetry it is just \[x=-\frac{b}{2a}\]
so 2?
no there is a minus sign in the formula
oh so x=-2?
\[x=-\frac{8}{2\times 2}\\ x=-2\]
What is the standard form equation of the line shown below? −3x + 2y = 5 3x − 2y = −5 y − 4 = three halves(x − 1) y = three halvesx + five halves
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you need the slope first you know how to find it?
y=mx+b?
that is the "slope intercept" form not standard form but in any case you need \(m\) (the slope) first
what is the standard form again ?
standard form will be one of your first two choices \[ax+by=c \]
im not understanding how i would use it
in fact we don't have to do any work at all for this one since only choice B is in standard form just pick that one and move on
Simplify open parentheses x to the 2 fifths power close parentheses to the 5 sixths power. x to the 37 over 30 power x to the 13 over 30 power x to the 10 elevenths power x to the 1 third power
i really appreciate you helping me <3
\[\huge (b^m)^n=b^{m\times n}\] is what you need for this one, i.e.multiply the exponents
yw
so what would the b be?
multiply \[\frac{2}{5}\times \frac{5}{6}\]
in this case \(b\) is \(2\)
do i cross multiply?
\[\huge (2^{\frac{2}{5}})^{\frac{5}{6}}\] \[\huge 2^{\frac{2}{5}\times \frac{5}{6}}\] hell no
multiply just means multiply
so\[\frac{ 10 }{ 30 }\]
\[\frac{2}{5}\times \frac{5}{6}\] we can cancel stuff too
the five
\[\frac{2}{\cancel{5}}\times \frac{\cancel{5}}{6}=\frac{2}{6}\] is a start
then you can cancel the 2 as well
or you could cancel here \[\frac{1\cancel{0}}{3\cancel{0}}=\frac{1}{3}\]
either way you get \(\frac{1}{3}\) and also you do NOT cross multiply
ok gotcha cx makes more sense now
whew final answer \[\huge 2^{\frac{1}{3}}\]
What is the simplified form of the quantity 12 z-squared minus 7z minus 12 over the quantity 3 z-squared plus 2z minus 8 ? 4z plus 3 over z plus 2 4z minus 3 over z plus 2 4z plus 3 over z minus 2 4z minus 3 over z minus 2
lol
wait wouldnt it be x1/3
\[\frac{12z^2-7z-12}{3z^2+2z-8}\] factor and cancel
hold on let me go back and look
yeah sorry \[\huge x^{\frac{1}{3}}\] the base was x, not 2
ahh gotcha
for the last one you have to factor and cancel i suck at factoring, but i am good at cheating http://www.wolframalpha.com/input/?i=\frac{12z^2-7z-12}{3z^2%2B2z-8}
i dont understand how to use that xD
this will work better http://www.wolframalpha.com/input/?i=%2812z^2-7z-12%29%2F%283z^2%2B2z-8%29 apparently it is \[\frac{4z+3}{z+2}\]
A?
click on the link to the second one and see how i wrote it in wolfram
yeah A
questions are all over the map must be an on line course ...
What is the simplified form of the seventh root of x times the seventh root of x times the seventh root of x times the seventh root of x? this one would be \[\sqrt[7]{4x}\] right?
no
yea it is XD
and oh i thought it was
one answer is \[x^{\frac{4}{7}}\]
another is \[\sqrt[7]{x^4}\]
the power is four, not the coefficient
\[x\times x\times x\times x=x^4\]not \(4x\)
4 times the seventh root of x x to the four-sevenths power the seventh root of 4x x to the seven fourths power
thes are the answers
\[\huge \sqrt[7]{x^4}=x^{\frac{4}{7}}\]
make that a B
Which of the following represents the zeros of f(x) = 6x3 + 25x2 - 24x + 5? -5, one third, one half 5, -one third, one half 5, one third, - one half 5, one third, one half
cheat like crazy for this one
http://www.wolframalpha.com/input/?i=+6x3+%2B+25x2+-+24x+%2B+5%3D0
\[\{-5,\frac{1}{2},\frac{1}{3}\}\]
so A?
otherwise you have to figure out that it factors as \[(3 x-1) (2 x-1) (x+5)\]
yeah A
Use the graph below for this question: What is the average rate of change from x = −1 to x = −2?
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\[5-7=-2\]
although the question is confusing since it says "from -1 to -2" which is backwards
maybe they want you to say 2, i am not clear on that the question is ill posed
not uncommon for an on line class btw
sorry i was talking to my brother
i gotta run now good luck with the rest keep posting in a new thread, i am sure you will get lots of answers
thank you so much!!!
yw any time!

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