Question

if x^2 + px - 5 =0 and x^2 + qx + 5 =0 have a common root the value of (p^2-q^2)=?

Answer 1

first find the roots of both equations & then
the middle term=\[(\alpha+\beta)x\]
wht u gt as roots in both of the equation put the values in the expression above

Answer 2

let the roots of first equation be \[x_1 , y_1\]& the roots of the second equation be\[x_2 , y_2\]write them as follows\[(x_1+y_1)^2-(x_2-y_2)^2\]

Answer 3

only thinking them as this

Answer 4

Hey i Think there is some formula if they have CR

Answer 5

bt dude i m nt sure :/

Answer 6

@mukushla @experimentX @Callisto m i correct???

Answer 7

@mathslover m i right????

Answer 8

@Yahoo!
exactly 'one' commen root?

Answer 9

May Be Two

Answer 10

first step must be to find the roots .. of both the eqn ..

Answer 11

as mentioned by @jiteshmeghwal9

Answer 12

@mathslover plz first tell me that i m correct or nt ????????????????????

Answer 13

@jiteshmeghwal9 please wait u will get your answer by your own soon

Answer 14

first equations roots\[\alpha={-p + \sqrt{p^2+20}\over2}\]\[\beta={-p-\sqrt{p^2+20}\over2}\]

Answer 15

second eqn roots

Answer 16

@experimentX what do you think for the next step?

Answer 17

second equations roots\[\alpha={-q + \sqrt{q^2-20}\over2}\]\[\beta={-q-\sqrt{q^2-20}\over2}\]

Answer 18

huh??

Answer 19

\[p={-p+\sqrt{p^2+20}\over2}+{-p-\sqrt{p^2+20}\over2}\]\[q={-q+\sqrt{q^2-20}\over2}-{-q-\sqrt{q^2-20}\over2}\]

Answer 20

put the values of 'p' in the equation to solve ur question:)

Answer 21

@Yahoo! any options given?

Answer 22

I knw the final answer

Answer 23

can u tell it?

Answer 24

wht is it @Yahoo! ????

Answer 25

20

Answer 26

can u plz try mine method & tell me wht u gt?????

Answer 27

ok wait i did wrong there. .. posting right one

Answer 28

I am getting \(\large{p-q=\sqrt{p^2+20}-\sqrt{q^2-20}}\)

Answer 29

i want p^2 - q^2?

Answer 30

yes wait..

Answer 31

\[\left( {-p+\sqrt{p^2+20 }\over2}+{-p-\sqrt{p^2+20}\over2} \right)^2-\left( {-q+\sqrt{q^2-20}\over2}+{-q-\sqrt{q^2-20}\over2}= \right)\]=??????????

Answer 32

anyone can see my reply??????????

Answer 33

if u solve this u must gt ur answer @Yahoo! :)

Answer 34

Hi everyone well let me tell u all the method to find the common root
May be @mukushla
will be familiar to it............

We get this expression using method of cross multiplication .........

The method says :

Let the common root be a

Then put the value of x = a in both eq. and equate them as both of them are roots of the expressions and then solve both eq. using cross multiplication......

This will give u the value of a.....

Answer 35

i guess 20 ?

Answer 36

check this...
the condition for 2 quadratic equation \(ax^2+bx+c=0\) and \(Ax^2+Bx+C=0\) for have 2 common roots is \(a/A=b/B=c/C\) but for our case this is not true so there is just one root in commen...

the condition for 2 quadratic equation \(ax^2+bx+c=0\) and \(Ax^2+Bx+C=0\) for have 1 common roots is

\((cA−aC)^2=(bC−cB)(aB−bA)\) it gives \(p^2-q^2=-20\) if im not wrong

@Yahoo!
try to work it out