Question

What two numbers whose product is -12 and sum of 9

Answer 1

Hint:

ab = -12
a + b = 9

Answer 2

Yes I no that but I can't seem to find the two number

Answer 3

2nd Hint:

a = 9 - b

Answer 4

How do you find b

Answer 5

b = -12/a

Answer 6

-21 and 9?

Answer 7

Where'd you get those numbers from?

Answer 8

I did something wrong

Answer 9

I don't no how to do this

Answer 10

Well, that's because you don't know the secret trick.

Answer 11

And that is

Answer 12

ab = -12
a + b = 9

Substitute a into the first equation to get

\((9-b)b = -12 \\
-b^2 + 9b = -12 \\
-(b^2 - 9b) = -12 \\
b^2 - 9b = 12 \\
b^2 - 9b - 12 = 0






\)

Answer 13

It's a quadratic equation

Answer 14

Sou solve from there ?

Answer 15

Yes. You might want to try completing the square for this.

Answer 16

\(b^2 - 9b = 12 \)

Answer 17

How do you solve to get the two numbers from here?

Answer 18

Add 81/4 to both sides

\(b^2 - 9b + \frac{81}{4} = 12 + \frac{81}{4}\)

Answer 19

How did you get 81/4

Answer 20

you dontt even need to do all that. just make a factor tree for -12 and see what two pairs add to 9

Answer 21

I got 81/4 by dividing the coefficient of the middle term by 2, then squaring it.

Simplify the left side into a binomial:

\((b - \frac{9}{2})^2 = 12 + \frac{81}{4}\)

Answer 22

Taking the square root of both sides to get

\(b - \frac{9}{2} = \sqrt{12 + \frac{81}{4}}\)

Answer 23

Then adding 9/2 to both sides to get:

\(b = \sqrt{12 + \frac{81}{4}} + \frac{9}{2}\)

Answer 24

Actually it's supposed to be + or -

Answer 25

\(b = \pm \sqrt{12 + \frac{81}{4}} + \frac{9}{2}\)

Answer 26

Now all we have to do is simplify that

Answer 27

\(b = \pm \sqrt{\frac{48}{4}+ \frac{81}{4}} + \frac{9}{2}\)

Answer 28

\(b = \pm \sqrt{\frac{48 + 81}{4}} + \frac{9}{2}\)

Answer 29

\(b = \pm \sqrt{\frac{129}{4}} + \frac{9}{2}\)

Answer 30

\(b = \pm \frac{\sqrt{129}}{\sqrt{4}} + \frac{9}{2}\)

Answer 31

\(b = \pm \frac{\sqrt{129}}{2} + \frac{9}{2}\)

Answer 32

\(b = \frac{\sqrt{129} + 9}{2}\)

Answer 33

Good luck finding a

Answer 34

Better yet use a = 9 - b to find a

Answer 35

\(a = 9 - \frac{\sqrt{129} + 9}{2}\)

Answer 36

\(a = \frac{18}{2} - \frac{\sqrt{129} + 9}{2}\)

Answer 37

@Hero
ab = -12
a + b = 9
\[\large{\color{blue}{(a+b)^2=81}}\]
\[\large{\color{red}{a^2+b^2+2ab=81}}\]
\[\large{\color{magenta}{a^2+b^2+2(-12)=81}}\]
\[\large{\color{brown}{a^2+b^2=81+24}}\]
\[\large{\color{green}{a^2+b^2=105}}\]


\[\large{\color{orange}{a^2-b^2=\sqrt{(a^2+b^2)^2-4a^2b^2}}}\]
\[\large{\color{blue}{a^2-b^2=\sqrt{(105)^2-(144*4)}}}\]
\[\large{\color{brown}{a^2-b^2=102->\textbf{Approx.}}}\]


\[\large{\color{blue}{a^2+b^2=105}}\]
\[\large{\color{red}{a^2-b^2=102}}\]
\[\large{\color{orange}{a^2=105-b^2}}\]
\[\large{\color{brown}{\textbf{Put this value of a^2 in the second equation of a^2-b^2}}}\]
\[\large{\color{red}{105-b^2-b^2=102}}\]
\[\large{\color{orange}{-2b^2=-207}}\]
\[\large{\color{magenta}{b^2=\frac{-207}{-2}}}\]
\[\large{\color{blue}{b=\sqrt{\frac{207}{2}}}}\]
\[\large{\color{green}{b=10.17}}\]
\[\large{\color{red}{a=9-10.17=-1.17}}\]

Answer 38

I don't know whether i am right or wrong..

Answer 39

Yeah, but I still have exact vaules

Answer 40

Yes you have them i am just off with .11 for product

Answer 41

Nice colors

Answer 42

thanks... well yes your's one gives b = 10.17 but a is giving something wrong

Answer 43

Well, both a and b can be either positive or negative

Answer 44

but a is something bigger than 12 at least...

sorry got to go for school now... if i would not then there will be a stick ready for my body .. :)

Answer 45

given ab = -12

but product of -19.17 and 10.17 is not near to 12

Answer 46

*-12

Answer 47

I know what I did wrong now.

\(a = \frac{18 - \sqrt{129} - 9}{2}\)

Answer 48

wow

Answer 49

lol

Answer 50

what is wrong with the quadratic formula?

Answer 51

\(x^2+9x-12=0\) etc

Answer 52

Nothing.

Answer 53

Well...nobody likes using it

Answer 54

You cant use factoring for this?

Answer 55

Therefore,

a = \(\large\frac{9 - \sqrt{129}}{2}\)
b = \(\large\frac{( 9+ \sqrt{129}}{2}\)

Answer 56

You can use factoring, quadratic formula, or complete the square for any quadratic.