Question

q

if p, q, r, s are non-zero numbers

p, q are the roots of x^2 + rx + s
r, s are the roots of x^2 + px + q

what is the value of p + q + r + s?

Answer 1

@dan815 @amistre64 @hartnn

Answer 2

Sum of roots for \(\Large ax^2+bx+c\) will be \(\Large -\dfrac{b}{a}\)

Answer 3

so sum of roots for x^2 + rx + s = ... ?

Answer 4

-r

Answer 5

= p + q

Answer 6

yes

Answer 7

also r + s = -p

Answer 8

thats correct

Answer 9

p + q + r + s = -(r + p)?

Answer 10

i'm not able to proceed

do i have to plug in the values of p or q and r or s into the equation?

Answer 11

i would say -(r+p) is the final answer...is a numeric answer expected?

Answer 12

yes, a numeral.

Answer 13

p + q + r + s = -r+r+s = s

similarly,
p + q + r + s = -p+p+q = q

which means s=q
hmm

Answer 14

p, q are the roots of x^2 + rx + s
r, s are the roots of x^2 + px + q
(x-p)(x-q)=x^2+rx+s
x^2+(-q-p)x+qp=x^2+rx+s
-q-p=r
qp=s

(x-r)(x-s)=x^2+px+q
similarily
-r-s=p
sr=q
------------------4 system of equations
-q-p=r
qp=s
-r-s=p
sr=q

Answer 15

4 unknowns, linearly independant so solved

Answer 16

with s=q
p=r=1

and -(p+r) =-2

Answer 17

p + q + r + s = s
2 + q + s = s

q = -2 = s

Answer 18

yes,
we allready knew
p + q + r + s = -(r+p) = -2

Answer 19

thank you!

Answer 20

welcome ^_^