Find all integers k such that the trinomial can be factored over the integers.
x2 − kx + 10
(smallest value)

(largest value)

Question

Find all integers k such that the trinomial can be factored over the integers.
x2 − kx + 10
(smallest value)

(largest value)

mr.math · Answer

You need to make ${k^2-40}$ a completer square.

mr.math · Answer

Obviously $k^2-40$ has to be greater than or equal to zero, which excludes all positive integers less than 6.

mr.math · Answer

There's no largest value, k can be a very large number.

mr.math · Answer

The smallest positive integer k such that the quadratic equation can be factored over the integers is 7 because $7^2−40=9$, which is a complete square.