If $\sin \theta ,\cos \theta$  are the roots of the equation $x^2+px+q=0$then $p^2=$$kq+m$ then k+m=

Given equation is  $x^2+px+q=0$

$\sin \theta ,\cos \theta$  are the roots of given equation

Sum of the roots is $\sin \theta +\cos \theta =-p,$ ….. ( 1 )

Product of the roots is $\sin \theta \cos \theta =q$  …… ( 2 )

From ( 1 ):

$\sin \theta +\cos \theta =-p,$

Squaring on both sides, we get

$\Rightarrow {\sin }^2\theta +{\cos }^2\theta +2\sin \theta \cos \theta =p^2\left(\because {\sin }^2\theta +{\cos }^2\theta =1,\sin \theta \cos \theta =q\right)$  

$\Rightarrow 1+2q=p^2$

$\therefore p^2=2q+1$