Finding all solutions of an expression and expressing them in the form $a+bi$

Question

$$6x^2+12x+7=0$$

Steps I took:

$$\frac { -12\pm \sqrt { 12^{ 2 }-4\cdot6\cdot7 } }{ 12 } $$

$$\frac { -12\pm \sqrt { -24 } }{ 12 } $$

$$\frac { -12\pm i\sqrt { 24 } }{ 12 } $$

$$\frac { -12\pm 2i\sqrt { 6 } }{ 12 } $$

I don't know where to go from here to arrive at the correct answer...

@Macavity
The correct answer should be $\frac { -6\pm \sqrt { 6 } i }{ 6 } $

I don't see it in what I arrived at... — Cherry_Developer, Sep 22 '14 at 08:16
Divide both your numerator and denominator by $2$ if you want it in that form. — Macavity, Sep 22 '14 at 08:17

score 4 · Accepted Answer · answered Sep 22 '14 at 08:17

4

Almost done $$\frac { -12\pm 2i\sqrt { 6 } }{ 12 }=\frac{-12}{12}\pm\frac{2i\sqrt6}{12}=-1\pm i\frac{\sqrt6}{6} $$

answered Sep 22 '14 at 08:17

Adi Dani

Thank you. I didn't understand why the answer was listed as $\frac { -6\pm \sqrt { 6 } i }{ 6 } $ when the instructions clearly said "... in the form $a+bi$"
So would my answer have been wrong on a test?
– Cherry_Developer Sep 22 '14 at 08:19
@Cherry_Developer I would say that strictly speaking, yes, your answer is incomplete. I would remove some, but not all points from it. – 5xum Sep 22 '14 at 08:32
1

Strictly following the instructions should result in "$-1+\frac{\sqrt6}6i$ and $-1+(-\frac{\sqrt6}6)i$". But only a sadist instructor would demand it. – Sep 22 '14 at 08:35
@YvesDaoust If someone answers $\frac{a+bi}{c}$ knowing that the form $\frac{a}{c}+\frac bci$ is only one step away, then the answer should be considered correct. If he doesn't, then points should be taken away. – 5xum Sep 22 '14 at 11:37

score 3 · Answer 2 · answered Sep 22 '14 at 08:16

3

Hint:

$$\frac{a+b}{c} = \frac ac + \frac bc$$

answered Sep 22 '14 at 08:16

5xum

score 1 · Answer 3 · answered Sep 22 '14 at 08:16

1

In this case $a=-1$ and $b=\frac{\sqrt{6}}{6}$ or $b=-\frac{\sqrt{6}}{6}$

answered Sep 22 '14 at 08:16

qwerty314

3 Answers3