Question

if two equations x²-Kx-21=0 and x²-3Kx+35=0 have a common root and J>0 then value of K is

Answer 1

First of all I didn't understand the thing J>0 .
It should either be D>0 or K>0.
Anyways I go on further.

Let the Common root of both the equations is 'R'
Therefore R will satisfy both the equations
R^2-KR-21=0 --(1)
R^2-3KR +35 =0. --(2)

Equating (1) and (2)
-KR-21 = -3KR +35
2KR=56.
KR=28
R=28/K

Satisfying this value of R in (1)
(28/K)^2 -K(28/K) -21=0
784/K^2 -28 -21=0
784/K^2 =49
K^2 = 784/49

K=±22/7.
You can also say that K=±π

Hope you got your answer :)