Question

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

Answer 1

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.