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}
