How many integers are there between 1 and 100 that can decompose x ^ 2 + x-n into the product of two factors (). Choose a: 0 B: 1 C: 2 D: 9 e: 10

How many integers are there between 1 and 100 that can decompose x ^ 2 + x-n into the product of two factors (). Choose a: 0 B: 1 C: 2 D: 9 e: 10

D
X^2+X-N=(x-a)(x-b)
Then a + B = - 1
ab=-N
Because n is between 1 and 100
Nmin = 2, - 2 * 1 = - 2
Nmax = 90, - 10 * 9 = - 90
So n has nine values

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

The square of x-5x + a can be decomposed into the product of the first-order factors of two integer coefficients. How many values of the conditional integer a are there

There are countless values of A
For example, a = 6 X & # 178; - 5x + 6 = (X-2) (x-3) a = - 6 X & # 178; - 5x-6 = (X-6) (x + 1)