Suppose a, b, care three non-zero real numbers. The equation `x^2+(a+b+c)x+(a^2+b^2+c^2)=0`

Let a and b be non-zero real numbers. Then the equation : (ax^2 + by^2 + c)(x^2 - 5xy + 6y^2) = 0 represents :

Let a, b, c be non-zero real roots of the equation x^(3)+ax^(2)+bx+c=0 . Then

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

Let 'a' and 'b' be non-zero real numbers. Then, the equation (ax^2+ by^2+c) (x^2-5xy+6y^2) represents :

Let a,b,c be three non-zero real numbers such that the equation sqrt(3)a cos x+2b sin x=c,x in[-(pi)/(2),(pi)/(2)] has two distinct real roots alpha and beta with alpha+beta=(pi)/(3). Then,the value of (b)/(a) is