anonymous
  • anonymous
x^3 -2x^2+13x=0 leave in exact form no decimals approx
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
You could write the same equation as: x(x^2 - 2x + 13) = 0 so one root is x = 0 and the others are the roots of x^2 - 2x + 13 =0 equation which are (1 - 2sqrt3) i and (1 + 2sqrt3 i)
anonymous
  • anonymous
did you solved this using quadratic formula negative b + or - square root b^2 - 4ac over 2a?
radar
  • radar
I believe he did and he simplified the answer.

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anonymous
  • anonymous
i tried that i did broke it down i got 2+ or - sqrt-48 over 2 times "a" which is 2 but when you divide the top (2+ or - sqrt-48) i got 24 which breaks down to to 2i sqrt 6 how did he get the 3?
radar
  • radar
\[\sqrt{-48}=\sqrt{16\times-3}\]
radar
  • radar
\[\sqrt{16}\times \sqrt{-3}\]\[4\sqrt{-3}\]
radar
  • radar
does that simplification rings a bell?
anonymous
  • anonymous
yeah i get it now its hard when someone just leaps from one spot to another
radar
  • radar
I haven't double checked but nikola usually gets it right. Good luck
anonymous
  • anonymous
Sweets, http://en.wikipedia.org/wiki/Quadratic_equation a=1 b=(-2) c=13 b^2 - 4ac = (-2)^2 - 4*1*13 = -48 which is smaller than 0,so roots are complex and can be calculated as : -b/2a + (sqrt [- (b^2 - 4ac)] /2a)*i -b/2a - (sqrt [- (b^2 - 4ac)] /2a)*i
anonymous
  • anonymous
yay nikola lol
radar
  • radar
And I have to agree with you sometimes simplified looks more complicated lol\[\sqrt{-48}=4\sqrt{-3}\] doesn't look to much more simple Hi
anonymous
  • anonymous
2+(sqrt[-2^2-4(1)(13)]/2(1) = 2+(sqrt[-48])/2 = so do I divide out the 2 from the bottom like so or no lol sorry for all this... 1+(sqrt[-24] then you break down the 24 to 4i sqrt 6
anonymous
  • anonymous
so 1+\[4i \sqrt{6} and 1-4i \sqrt{6}\]
anonymous
  • anonymous
that was suppose to be 2i sqrt6 not the 4 my bad
anonymous
  • anonymous
Sweets, a=1 b=(-2) c = 13 b^2 - 4ac = (-2)^2 - 4*1*13 = -48 < 0 so; -b/2a + (sqrt [- (b^2 - 4ac)] /2a)*i -b = -(-2) = 2 so -b/2a is 2/2*1 =1 sqrt [- [b^2 - 4ac) ] = sqrt [-(-48)] = sqrt48 which is 4sqrt3 (sqrt [- (b^2 - 4ac)] /2a)*i is 4sqrt3 / 2 *1 = 2sqrt3 I hope this helps.
anonymous
  • anonymous
i have got 2+24i and 2-24i as the answer
anonymous
  • anonymous
yes thats correct nikola:)
anonymous
  • anonymous
Sweets,it s -b/2*a not -b/a :)
radar
  • radar
\[(-(-2)\pm \sqrt{(-2)^{2}-(4)(1)(13)})/2\]\[(2\pm \sqrt{4-52})/2\]\[(2\pm \sqrt{-48})/2\] can you take it from there?
anonymous
  • anonymous
Oooooo lol i see i see
anonymous
  • anonymous
you miss one thing it messes it all up lol
anonymous
  • anonymous
yeah...thats what math is all about:)
anonymous
  • anonymous
haha gotta love it
anonymous
  • anonymous
so th eanswer probably is 1+24i & 1-24i if i am not wrong:)
radar
  • radar
Continuing on.\[(2\pm(\sqrt{16\times-3})/2\] \[(2\pm(\sqrt{16}\sqrt{-3})/2\]\[(2\pm(4\sqrt{-3})/2\] now do the division\[1\pm2\sqrt{-3}\]
anonymous
  • anonymous
how did u get -3 there? under the root???
radar
  • radar
I would leave it there are you could go further and do this. Convert the radical as follows:\[\sqrt{-3}=\sqrt{3 X-1}\]
radar
  • radar
The square root of -1 is the imaginary operator i so the final answer becomes:\[1\pm \sqrt{3}i\]
radar
  • radar
Did you understand I was trying to show in the radical 3 times a -1 ? and i left out the 2 so it should be\[1\pm2\sqrt{3}i\]
anonymous
  • anonymous
yeah i seen what you did 4 squared times 3 is 48 but you had to divide the 4 by 2 i get it
radar
  • radar
Yeahh!!!Now practice is the key. Notice that they did not want you to really get the value no decimals etc. so that is as far as you need to take it.
anonymous
  • anonymous
lol thank all of you so much. Im not as slow as i seem this was just a total brain fart
anonymous
  • anonymous
Im a visual learner so it helped when you showed :)
anonymous
  • anonymous
you're welcome sweets,good luck with your studies.

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