What binomial is a factor of this trinomial x2 plus 13x plus 4?

Answer 1

x2 + 13x + 4 = (x + 6½ + √38¼)(x + 6½ - √38¼).

To find this, we need to find p and q, where

p + q = 13, pq = 4.

4 = 42¼ - 38¼

= (6½ + √38¼)(6½ - √38¼); thus,

p = (6½ + √38¼), q = (6½ - √38¼).