Question

Find a so that

x^2 + ax + 1= 0 and
x^2 + x + a = 0

have a common root.

Answer 1

??? your question?

Answer 2

a common root being that they cross at a given x=0 point

Answer 3

x=1

Answer 4

just substitute and see

Answer 5

find a not x :)

Answer 6

its the common root

Answer 7

Common eg roots alpha and beta, one of them same in both equations.

Answer 8

but for all a x=1 is common?

Answer 9

U r right, I made a booboo...

Answer 10

x^2 + ax - 1= 0

Answer 11

ohhhhh

Answer 12

GN guys gotta go!
this site is realllllllllly addictive

Answer 13

x^2 + nx - 1= 0 and

x = \(\cfrac{-n \pm\sqrt{n^2+4}}{2}\) and factorize it in

x^2 + x + n = 0

x = \(\cfrac{-1\pm\sqrt{1-4n}}{2}\)

would this be useful?

Answer 14

\[-n + \sqrt{n^2+4}=-1+\sqrt{1-4n}\]
and fight with it tooth and nail?

Answer 15

i get n=0 perhaps?

Answer 16

http://www.wolframalpha.com/input/?i=y%3Dx^2+-+1++and+y+%3D+x^2+%2B+x

Answer 17

Doncha just love algebra?

Answer 18

my link dint linkate

Answer 19

when a=0; they root at -1

Answer 20

always remember, when anyone gives you a seemingly difficult question, the answer is either 1 or 0 :)

Answer 21

???

Answer 22

x^2 + 0x - 1 and x^2 +x +0 have the same root of x=-1

Answer 23

U r right, I should have done it ur way...

Answer 24

Now heres the deal for common roots
Lets say two equations \(a_1x^2 +b_1x+c_1=0\) and \(a_2x^2 +b_2x +c_2=0\).
\[(b_1c_2 -b_2c_1)(a_1b_2-a_2b_1)=(c_1a_2 - c_2a_1)^2\]

So our equations are.
\[x^2 +ax+1=0\]\[x^2+x+a=0\]
That gives,
\[(a^2 - 1)(1-a) = (1-a)^2\]
\[a^2 -1 = 1-a \]
\[a^2 +a-2 =0\]
\[a = \frac{-1 \pm \sqrt{1 + 8}}{2}\]

Answer 25

my calc 1 teacher said, whenever you have a seemingly impossible equation, the answer is either 1 or 0

Answer 26

I got -i sqrt 3

Answer 27

Back later....

Answer 28

Myininaya, are you busy?

Answer 29

sort of
what do you want?

Answer 30

I have a question about your alternative method of grouping

Answer 31

one sec...

Answer 32

whats your question?

Answer 33

If you solve 3x^2 +8x + 2 = 0 using your method what do you get?

Answer 34

That's what I got. Okay. I was just checking

Answer 35

lol ok

Answer 36

Thank you :o)

Answer 37

I got:
\[x = -\frac{4+\sqrt{10}}{3}, \frac{-4+\sqrt{10}}{3}\]

Answer 38

thats good :)

Answer 39

estudier i like your question
i wish i had gotten to it first instead of amistre :(