If roots of `ax^2+2bx+c=0(a !=0)` are non-real complex and `a+c <2b.` then

Theorem : Let a, b, c in R and a ne 0. Then the roots of ax^(2)+bx+c=0 are non-real complex numbers if and only if ax^(2)+bx+c and a have the same sign for all x in R .

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, then

If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 + bx + c = 0 are non-real complex numbers, that

If coefficients of the equation ax^(2)+bx+c=0,a!=0 are real and roots of the equation are non-real complex and a+c

If coefficients of the equation ax^2 + bx + c = 0 , a!=0 are real and roots of the equation are non-real complex and a+c < b , then

Assertion (A) : If 3 + iy is a root of x^(2) + ax + b = 0 then a = -6 Reason (R) : If a, b , c are real and Delta lt 0 the roots of ax^(2) + bx + c = 0 are conjugate complex numbers

If 0

If the roots of equation ax^(2)+bx+c=0;(a,b,c in R and a!=0) are non-real and a+c>b. Then