1basic is like dis
let
f(x) = 13x^2 + 41 x + 37 \, \, \, \, and \, \, \, \, g(x)= 91 x^2 +67x + 13
now
f(-x) = 13(-x)^2 + 41 (-x) + 37 = 13 x^2 -41 x + 37
observin coeefecients of f(-x)
13 x^2 -41 x + 37
+ \,\, -\, \, \, \, +
coefficient of x^2 is 13 which is +ve
coefficient of x =-41 which is -ve
constant term = + ve
hence sign of f(-x) changes two times
from +ve to - ve and then -ve to + ve
f(x) = 13x^2 + 41 x + 37
here there is no change in signs of coefficient of x2 , x , and constant term
ie all are +ve
hence
no of positive roots = no of changes in signs of f(x) =p
no.o negative roots = no.o changes in signs of f(-x) = n
no.o complex roots = degree of f(x) - n-p =c
similarly u can continue for g(x) and other three options
