Question

Real solutions of the equation...
\[x^4+4x^3+2x^3=0\]
I get to
\[x^2(x^2+4x+2)=0\]
and get stuck

Answer 1

oops.... that's 2x^2

Answer 2

I don't think you can factor it down more, you're going to have to use the quadratic formula for the part inside the parentheses.

Answer 3

Factorise the x^2+4*x+2

Answer 4

and don't forget that 0 is a solution from the x^2 outside the parentheses

Answer 5

i attempted completing the square, but that didn't seem to give my the correct answer... it gives: \[x^2+4x+4=-2\]
then factoring gives: \[x^2(x+2)(x+2)=-2\]
am i on the right track here?

Answer 6

It needs to be equal to 0, otherwise it doesn't tell you very much about the equation

Answer 7

Why not use the quadratic formula to solve the factor \[(x ^{2}+4x+2)=0\]

Answer 8

completing the square requires you to subtract "c" (2) from both sides and divide "b" (4) by 2 then square it. completing the square...

Answer 9

\[x=2\pm \sqrt{2}\]

Answer 10

-b = -4, does it not?

Answer 11

yes

Answer 12

how does x=2 +/- sqrt (2) then?

Answer 13

you can factor out a 2 from the quadratic formula once you simplify it. What are you getting?

Answer 14

Well maybe it is \[-2\pm \sqrt{2}\]

Answer 15

\[-4\pm \sqrt 8 \over 2\]

Answer 16

okay. my problem was simplifying then... i think i just saw what i was doing...

Answer 17

\[\sqrt{8}= \sqrt{2*4}=\sqrt{2}*\sqrt{4}=2*\sqrt{2}\]

Answer 18

taking two of the 3 2's necessary to make 8 would bring out a 2 correct? then divide by 2.... leaving one 2 in the square and one outside. simplified would be 1 +/- sqrt(2) over 1 right?

Answer 19

\[-2+-\sqrt{2}\]

Answer 20

+/-

Answer 21

thanks. both of you.