One of the roots of the equation x^2 + kx - 6 = 0 is 3, and k is constant

In order to solve this problem, we need to use the factor and remainder theorem. Suppose we have a quadratic equation of Q (x) and a binomial x-a=0, where a is a constant such that x=a. When you substitute x=a to the quadratic equation, you use the answer as basis. Whatever the answer is, is the remainder. If the answer is zero, that means that x=a is a factor.

In this case, we substitute x=3 to the quadratic equation and equate to zero to find k.

Q (x) = x²+kx-6

Q (3) = 3²+k (3) - 6 = 0

k = - 1

The value of k is - 1.