Question

URGENT!!
for the quadratic equation it says,,,

The solutions of ax^2 +bx+c=0,where a (then a funny sign!) 0, are given by...(then it says the formula).....
what is that funny sign??? and what if the sum is in minus?? and last but not least wat does that +- sign mean??
THNX!!

Answer 1

\[ax^2+bx+c=0, a\ne0\]Is that what you see? the funny sign means "does not equal"

Answer 2

the solutions are given by
\[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]

Answer 3

ye after the a is the funny sign

Answer 4

the \(\pm\) means "plus or minus" — there are actually two solutions, one with the plus, one with the minus.

Answer 5

It is just a more compact way to write it than
\[x = \frac{-b + \sqrt{b^2-4ac}}{2a},x=\frac{-b-\sqrt{b^2-4ac}}{2a}\]

Answer 6

oh,thnx so we shud give two answers??
and work it out twice?
and what if the sum your given is in minus is it the same method...

Answer 7

Yes, a quadratic always has 2 solutions (though in some cases they are the same value).

I'm not sure what you mean by "if the sum your given is in minus" — can you give me an example?

Answer 8

sure.lets say\[3x^2-4x-2=0\]

Answer 9

Okay, in this case, \(a = 3, b= -4, c = -2\)

Answer 10

oh im so stupid.obviously
so then you work out wats in the square root,then square root it,then -b plus the answer,then share by 2a?

Answer 11

For your example:
\[x = \frac{-(-4)\pm\sqrt{(-4)^2-4(3)(-2)}}{2*3} = \frac{4\pm\sqrt{16+24}}{6}=\frac{4\pm2\sqrt{10}}{6}\]

Answer 12

$$
\sqrt{9} = \sqrt{(3)^2} = +3\\
\sqrt{9} = \sqrt{(-3)^2} = -3\\
\text{so, thus}\\
\color{blue}{\sqrt{9} = \pm 3}
$$

Answer 13

wat wheres the root 9 from jdoe

Answer 14

He's just illustrating why the \(\pm\) business is there.

Answer 15

so how dya wite the final answer?

Answer 16

that is true for any value "coming out" of the square root, reason why is a \(\pm\)

Answer 17

aha thnx!

Answer 18

Well, as I wrote it is one way. Another would be \(x=\frac{1}{3}(2+\sqrt{10}), x=\frac{1}{3}(2-\sqrt{10})\)

Answer 19

x = -0.387426, x = 1.72076 would be another

Answer 20

I generally prefer symbolic, exact solutions (like the ones with the square root signs) to the numeric, unless a number is what is required.

Answer 21

Do you want another one to try? I'll check your work...

Answer 22

oh thnx so much but why didnt you add the 16 and 24 in the 'post 11' up

Answer 23

Oh, I did, then I simplified it without showing the intermediary step, because I was afraid of getting cut off on the right side of the window.

\[\sqrt{16+24} = \sqrt{40} = \sqrt{4*10} = \sqrt{4}*\sqrt{10} = 2\sqrt{10}\]

Answer 24

OMG i have no idea how root 40 gets to 2 root 10
sorry..

Answer 25

Even with me showing you the steps there?

Answer 26

oh so it gets to 4 times 10 why cant u leave it ther

Answer 27

How are you with exponents? Square roots are just fractional exponents, specifically\[\sqrt{x} = x^{1/2}\]
We know that \[(ab)^n = a^nb^n\]so \[(ab)^{1/2} = a^{1/2}*b^{1/2}\] and so \[\sqrt{ab} = \sqrt{a}*\sqrt{b}\]

Answer 28

You could leave it as \(\sqrt{40}\) but usually you want to simplify/reduce as much as possible.

Answer 29

right thnx sososososo much!!!

Answer 30

you're welcome!

Answer 31

hey can i put in another q?
how do you know when to use which formula for workin out triangles...sine,trig,cosine..

Answer 32

that's kind of a broad question! One helpful mnemonic is

SOH CAH TOA

Sin = Opposite over Hypotenuse
Cos = Adjacent over Hypotenuse
Tan = Opposite over Adjacent

"Opposite" here refers to the length of the side opposite the angle of which you are taking the sin, cos, tan; similarly "Adjacent" refers to the length of the side adjacent to the angle

Answer 33

ye i know but im talkin about for which triange and to find wat eg side or angle are you supposed to use each method for?

Answer 34

Sorry, that's not really a short answer question...

Answer 35

oops ok...lets say if u know 2 angles so u use sohcahtoa
1 angle=cosine?

Answer 36

well, SOHCAHTOA only applies if you have a right triangle. If you have arbitrary angles, then the law of sines or law of cosines might help. If you just need to find the 3rd angle, remember that the sum of the interior angles of a triangle is always 180 degrees. In general, the sum of the interior angles of an n-sided polygon is (n-2)*180, so a triangle is 180, a rectangle or trapezoid is 360, a pentagon is 540, etc.