A,B,C are real numbers ,a not equal 0 and the quadratic equation ax^2+BC+C=0 has no real roots,then. (A) a+b+C>0. B. a(a+b+C)>0. C b(a+b+C)>0. D C(a+b+C)>0. (Chose the two correct alternative {two answer are there})

Let me give you a shorter proof.

As there is no real zeroes, f(x) is either greater than zero or less than zero, for all x. As f(x) is continuous, it cannot change sign because it would imply a zero.

Consider x=1, f(1)=a+b+c

So f(0)

f(0) = c

So, c

This argument will enable you to prove more statements like this

a(a+c)^2+b(a+c)+c