Question

Solve –2x2 +3x – 9 = 0. (solving quadratic equation with complex numbers).

Answer 1

Ok, so use the quadratic formula. What is that formula?

Answer 2

\[\begin{array}{*{20}c} {x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} & {{\rm{when}}} & {ax^2 + bx + c = 0} \\ \end{array}\]

Answer 3

right. So apply that formula with your equation.

Answer 4

remember how I said last time to find out what a b and c are and plug them into the formula

Answer 5

yah.

Answer 6

You will get two answers for x

\[\pm \]

That signs means you have to do it two times.

One time with +

and then a second time with -

Answer 7

okay , so first I factor 3x?

Answer 8

Is this your equation?\[–2x^2 +3x – 9 = 0\]

Answer 9

yes, srry I forgot to put ^.

Answer 10

Ok you don't need to factor or do anything at all to find out what a b and c are
\[–2x^2 +3x – 9 = 0\]
then a b and c are
\[ax^2 +bx + c = 0\]

Answer 11

I'll give you a to help you out
\[a=-2\]

Answer 12

can you tell me what b and c are?

Answer 13

Very nice Romero.

Answer 14

B is 3x and C is 9?

Answer 15

We just want numbers for a b and c so no x

Answer 16

ok.

Answer 17

so\[b=3\]

Answer 18

oh so I was right

Answer 19

just with out the X

Answer 20

also see how I also included the negative sign in a
\[a=-2\]
you also have to included for c

Answer 21

Yeah and you forgot the negative sign for c

Answer 22

ok.

Answer 23

\[a=-2\]
\[b=3\]
\[c=-9\]
correct?

Answer 24

yep.

Answer 25

So now, apply the formula Romero gave you above. What do you get?

Answer 26

Now\[{x = \frac{{ - b \pm \sqrt {b^2 - 4ac} }}{{2a}}} \] we want to solve for x using the quadratic formula

Answer 27

idk, it's going to take a while....

Answer 28

It should take you a while at first... this really hard math but as long as you keep at it and solve for x you will get it

Answer 29

Well, this is why you have these problems: to practice. We all have to do lots of these to get fast at them. So off you go!

Answer 30

k.

Answer 31

Remember do it two times

\[{x = \frac{{ - b- \sqrt {b^2 - 4ac} }}{{2a}}}\]
\[{x = \frac{{ - b + \sqrt {b^2 - 4ac} }}{{2a}}}\]

Answer 32

where does A=-2 go? on the outside right?

Answer 33

nm I found it

Answer 34

so it shud look like -3+- √3^2 4(-2)(-9)/2(-2)?

Answer 35

???

Answer 36

\[ \frac{-3 \pm \sqrt{3^2 - 4(-2)(-9)}}{2(-2)} \]
yes. Now simplify.

Answer 37

okay ty

Answer 38

okay so now it's -3 +-√9 +72 /-4?

Answer 39

sign error. Check your calculation.

Answer 40

hint: it's inside the parentheses the error

Answer 41

why what's wrong?

Answer 42

okay anyway , now it's -3 +-√81/-4?

Answer 43

\[-a*-b=+c\]

Answer 44

Nope. --- = -, not --- = +

Answer 45

isk what that means? can you expain?

Answer 46

That means negative times a negative is a positive but
inside the parentheses you have negative times negative times negative

Answer 47

so two negatives will give you a positive times another negative will give you a negative

Answer 48

so negative 72?

Answer 49

\[{x = \frac{{ - 3 \pm \sqrt {3^2 - 4(-2)(-9)} }}{{2(-2)}}}\]
\[{x = \frac{{ - 3 \pm \sqrt {9 - 72} }}{{-4}}}\]

Answer 50

yeah

Answer 51

ty.

Answer 52

so now it'a -3+-√-63 /-4...now wat?

Answer 53

it's*

Answer 54

\[{x = \frac{{ - 3 \pm \sqrt {-63} }}{{-4}}}\]

Answer 55

From there we want to get the complex number

Answer 56

We get it from the negative sign inside the square root

Answer 57

\[\sqrt{-1}=i\]

Answer 58

what does that mean andf where did that come from?

Answer 59

\[x=\frac{-3 \pm \sqrt{-63}}{-4}\]
\[x=\frac{-3 \pm i \sqrt{63}}{-4}\]

Answer 60

okay now what do we square root of 63?

Answer 61

I really don't know what it means or how to explain it that well but basically the \[\sqrt{-1}=i\]
and yeah you are right we can square root 63 now because now we don't have to worry about the negative value

Answer 62

If you want to learn more about complex numbers you just wikipedia it.

Answer 63

okay , thank you for all ur help :D

Answer 64

\[x=\frac{-3 \pm i 3\sqrt{7}}{-4}\]


\[x=\frac{-3}{-4} \pm \frac{3i \sqrt{7}}{-4} \]
\[x=\frac{3}{4} \pm \frac{3i \sqrt{7}}{-4} \]
\[x=\frac{3}{4} + \frac{3i \sqrt{7}}{-4} and, x=\frac{3}{4} - \frac{3i \sqrt{7}}{-4}\]

Answer 65

that's noot one of my choices?

Answer 66

what are your choices?

Answer 67

hold on.

Answer 68

The problem is that we might of simplified it differently. I mean 3/4 actually equals 0.75 and you can also change the squareroot of 7 so that might be it

Answer 69

x=3+-i√29/2 < and then the same but just -3
and then x=3+-i√23 and then the same just with -3 thses are my choies