**Answer:**

The given equation has TWO positive integer valued solutions, {6, 7}

**Step-by-step explanation:**

Here we are given two trinomial factors, each of which needs to be set equal to zero and in each case the resulting quadratic equation solved.

(x^2 - 7x + 11) has the coefficients {1, -7, 11}, and so the discriminant of this quadratic is b^2 - 4(a)(c), or 49 - 4(11), or 5.

Because this discriminant is positive, we know immediately that this quadratic has two real, unequal roots involving √5 (NO integer roots).

Next we focus on (x^2 - 13x + 42). The discriminant is b^2 - 4(a)(c), or

169 - 168, or 1. Again we see that there are two real, unequal roots:

+13 ± √1 +13 ± 1

x = --------------- or x = -------------

2 2

OR x = 14/2 = 7 (integer) or x = 12/2 = 6 (integer).

The given equation has TWO positive integer valued solutions, {6, 7}