Question

Justify if completing the square is a good method for solving
when the Discriminant is negative. Use any of your three
functions as an example and respond in complete sentences.
My beautiful function: x2-10x+24

Answer 1

@amistre64

Answer 2

@gorv

Answer 3

@jim_thompson5910

Answer 4

@mathstudent55

Answer 5

HALP WATER

Answer 6

What I am supposed to do?? Completing the square of that function?

Answer 7

i mean, when the discriminant is a negative, doesn't that mean the answer is going be a complex root thing?

Answer 8

wait, so what should i do?

Answer 9

which formula should i use to make it a "perfect square"?

Answer 10

When D is negative, you are surely going to get Complex Roots, do you have any doubt?

Answer 11

nope

Answer 12

what else should i write...

Answer 13

Are you trying to find x or doing what? What exactly you are doing?

Answer 14

justify if completing the square of that equation is good when your trying to get answer with a negative discriminant. Well i technically just "think" thats what it means, i came here to see if anyone could "understand" the question.

Answer 15

cause i have no idea what the hell that thing is saying.

Answer 16

Same here, but let us start completion of square method, do you know it?

Answer 17

somewhat

Answer 18

i keep forgetting that formula

Answer 19

That will do, don't worry.. :)

Answer 20

was it the one with a^2(y+h)-f or something?

Answer 21

or was it the other other one?

Answer 22

It is just:

\[(a+b)^2 = a^2 + 2ab + b^2 \\ (a-b)^2 = a^2 -2ab + b^2\]

Answer 23

:O

Answer 24

Just basic formulae.. :)

Answer 25

so this is useless?
(x-4)(x-6), x2-10x+24, b2-4ac, -102-4(1)(24), 100-96, 4

Answer 26

\(x^2 - 10x + 24\)

\(D = 100 - 96 = 4\) D is not negative.. :(

Answer 27

oh damn

Answer 28

WE SHALL USE ThE OTHER OTHER ONE

Answer 29

Choose function with D = negative..

Answer 30

x2-10x+28, b2-4ac: -102-4(1)(28), 100-112, -12.

Answer 31

ther

Answer 32

i made 3 extras XD

Answer 33

the discriminant is -12

Answer 34

yay...

Answer 35

Let amistre keep his point here, we should not do without his guidance.. :P

Answer 36

huzzah!

Answer 37

quadratic formula is a formula that is developed from completing the square ....

long way, complete the square; short way: use the formula

Answer 38

soooooo

Answer 39

Yeah I never thought it that way.. :(

Answer 40

so, we prove the formula by completing the square ....

Answer 41

Yep..

Answer 42

yeah...

Answer 43

wait so how do i input the information into the formula water gave me?

Answer 44

That is why I asked you if you are finding x then we have two methods to use.. We can use Quadratic Formula as well as Factorization if applicable.. :)

Answer 45

quadratic formula pls

Answer 46

Yes, you draw nice.. :P

Answer 47

thank you

Answer 48

i think amistre is writing a very long thingy

Answer 49

\[ax^2 + bx + c = 0\]
\[ax^2 + bx =-c\]
\[x^2 + \frac bax =-\frac ca\]
\[x^2 + \frac bax+\frac{b^2}{(2a)^2} =\frac{b^2}{(2a)^2}-\frac ca\]
\[(x+ \frac ba)^2 =\frac{b^2}{(2a)^2}-\frac ca\]
\[x+ \frac ba =\pm\sqrt{\frac{b^2}{(2a)^2}-\frac ca}\]
\[x=- \frac ba \pm\sqrt{\frac{b^2}{(2a)^2}-\frac ca}\]

Answer 50

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

Answer 51

oh that formula

Answer 52

moving the number to the other side

Answer 53

ugh, i dropped a 2

Answer 54

(x+b/(2a))^2 and work it thru

Answer 55

x2-10x+28, x2-10x=-28, (x2-10x+25)=-28+25, (x2-10x+25)=3, (x-5)2=-3,

Answer 56

is it that?

Answer 57

then you root it

Answer 58

\[\sqrt{x-5}^{2}=\sqrt{3}\]

Answer 59

\[x=- \frac b{2a} \pm\sqrt{\frac{b^2}{(2a)^2}-\frac ca}\]
\[x=- \frac b{2a} \pm\sqrt{\frac{b^2}{4a^2}-\frac ca}\]
\[x=- \frac b{2a} \pm\sqrt{\frac{b^2}{4a^2}-\frac {4ac}{4a^2}}\]
\[x=- \frac b{2a} \pm\frac{\sqrt{b^2-4ac}}{2a}\]

Answer 60

it seems your doing it another way....

Answer 61

im proving the formula is all by taking a general quadratic and algebraing it into the formula .... solving for x

Answer 62

i don't think i learnt that...

Answer 63

and D is technically equal to the inside of the sqrt, not the whole sqrt .... but i prefer to include the sqrt as water did

Answer 64

you didnt learn how to complete a square?

Answer 65

I'm just confused tis all

Answer 66

did you cover how to complete a square?

Answer 67

i think

Answer 68

wait I'm on the lesson thats called "completing a square"

Answer 69

well #### this

Answer 70

the method of completing the square, results in the quadratic formula .. it is the proof.

Answer 71

its just i never saw that "formula" while i tried to stay awake in class

Answer 72

hmmm, its either i seriously am being derby, or its just that i didn't learn it

Answer 73

i only learnt the thing i wrote

Answer 74

and then the +- 5 and 3

Answer 75

and then you figure both of those out

Answer 76

given: ax^2 + bx + c = 0

what is the first step in completing the square?

Answer 77

you move the c over to 0

Answer 78

which makes it -c

Answer 79

ax^2 + bx = -c

then?

Answer 80

then you divide bx by 2, and square that

Answer 81

nope, need to get rid of that a

Answer 82

oh

Answer 83

divide off the a

Answer 84

if a has a number other than 1

Answer 85

than you factor it

Answer 86

into a(x+bx)=-c

Answer 87

a=1 still works when you divide by it :)

x^2 + b/a x = -c/a

now we can do the halving thing

Answer 88

x2

Answer 89

yeah....

Answer 90

do you see that we divided both sides by a?

Answer 91

yep

Answer 92

ax^2 + bx = -c

x^2 + b/a x = -c/a

ok, now lets add the (b/2a)^2 to each side

x^2 + b/a x + (b/2a)^2 = (b/2a)^2 - c/a

whats next?

Answer 93

uhh

Answer 94

combining them all?

Answer 95

or like terms

Answer 96

cause i have definitely NOT learnt this

Answer 97

turning the left side into a (x+b/2a)^2 yes since it is not a perfect square on that side