Given that x2 + ax-12 = 0 can be decomposed into the product of the first-order factors of two integral coefficients, then the number of qualified integers a is______ ．

Given that x2 + ax-12 = 0 can be decomposed into the product of the first-order factors of two integral coefficients, then the number of qualified integers a is______ ．

When - 12 = 1 × (- 12), a = 11; when - 12 = 2 × (- 6), a = 4; when - 12 = 3 × (- 4), a = 1; when - 12 = 4 × (- 3), a = - 1; when - 12 = 6 × (- 2), a = - 4; when - 12 = 12 × (- 1), a = - 11

Write out the quadratic trinomial with X, the coefficient of x ^ 2 is 1, the constant term is 16, and it can decompose the factor, so the quadratic trinomial is

x²+8x+16;
x²-8x+16;
x²-10x+16;
x²+10x+16;
x²+17x+16;
x²-17x+16;
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Please write a quadratic equation of one variable with quadratic coefficient of 1 and sum of two real roots of 36
Please write a quadratic equation of one variable with quadratic coefficient of 1 and sum of two real roots of 3

Let ax ^ 2 + BX + C = 0
According to the meaning of the title
a=1
x1+x2=-b/a=3
If you solve this system of equations, you can see
a=1
b=-3
C = any real number
The original equation is
X ^ 2-3x + k = 0 (k is any real number)