It is known that the square of the equation x - ax + A + 3 = 0 has two equal real roots to find the value of A

It is known that the square of the equation x - ax + A + 3 = 0 has two equal real roots to find the value of A

x^2-ax+a+3=0
(x-a/2)^2+a+3-a^2/4=0
a+3-a^2/4=0
a^2-4a-12=0
(a+2)(a-6)=0
A = - 2 or a = 6

It is known that a, B and C are three real numbers which are not all zero, then the root of the equation x2 + (a + B + C) x + A2 + B2 + C2 = 0 is ()
A. There are two negative roots B. There are two positive roots C. There are two positive roots and one negative root d. There are no real roots

∵ △ = (a + B + C) 2-4 (A2 + B2 + C2) = - 3a2-3b2-3c2 + 2Ab + 2BC + 2Ac = - (A-C) 2 - (B-C) 2 - (a-b) 2-a2-b2-c2, and a, B and C are three real numbers which are not all zero, ∵ (A-C) 2 - (B-C) 2 - (a-b) 2 - ≤ 0, a2-b2-c2 < 0, ∵ △ < 0, ∵ the original equation has no real root, so D

Given that a, B and C are not all equal non-zero real numbers, the following three statements about the equation of X are correct
ax^2+(a-b)x+a-b/2-c/2=0,bx^2+(b-c)x+b-a/2-c/2=0,cx^2+(c-a)x+c-a/2-b/2=0
A at least one equation has real roots B at least one equation has no real roots C at most one equation has real roots d at most one equation has no real roots