Question

x^3 -2x^2+13x=0 leave in exact form no decimals approx

Answer 1

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)

Answer 2

did you solved this using quadratic formula negative b + or - square root b^2 - 4ac over 2a?

Answer 3

I believe he did and he simplified the answer.

Answer 4

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?

Answer 5

\[\sqrt{-48}=\sqrt{16\times-3}\]

Answer 6

\[\sqrt{16}\times \sqrt{-3}\]\[4\sqrt{-3}\]

Answer 7

does that simplification rings a bell?

Answer 8

yeah i get it now its hard when someone just leaps from one spot to another

Answer 9

I haven't double checked but nikola usually gets it right. Good luck

Answer 10

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

Answer 11

yay nikola lol

Answer 12

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

Answer 13

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

Answer 14

so 1+\[4i \sqrt{6} and
1-4i \sqrt{6}\]

Answer 15

that was suppose to be 2i sqrt6 not the 4 my bad

Answer 16

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.

Answer 17

i have got 2+24i and 2-24i as the answer

Answer 18

yes thats correct nikola:)

Answer 19

Sweets,it s -b/2*a not -b/a :)

Answer 20

\[(-(-2)\pm \sqrt{(-2)^{2}-(4)(1)(13)})/2\]\[(2\pm \sqrt{4-52})/2\]\[(2\pm \sqrt{-48})/2\] can you take it from there?

Answer 21

Oooooo lol i see i see

Answer 22

you miss one thing it messes it all up lol

Answer 23

yeah...thats what math is all about:)

Answer 24

haha gotta love it

Answer 25

so th eanswer probably is 1+24i & 1-24i if i am not wrong:)

Answer 26

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\[1\pm2\sqrt{-3}\]

Answer 27

how did u get -3 there? under the root???

Answer 28

I would leave it there are you could go further and do this. Convert the radical as follows:\[\sqrt{-3}=\sqrt{3 X-1}\]

Answer 29

The square root of -1 is the imaginary operator i so the final answer becomes:\[1\pm \sqrt{3}i\]

Answer 30

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\[1\pm2\sqrt{3}i\]

Answer 31

yeah i seen what you did 4 squared times 3 is 48 but you had to divide the 4 by 2 i get it

Answer 32

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.

Answer 33

lol thank all of you so much. Im not as slow as i seem this was just a total brain fart

Answer 34

Im a visual learner so it helped when you showed :)

Answer 35

you're welcome sweets,good luck with your studies.