Given that x = 1/2 is a root of the equation 2x^3 – 9x^2 + kx – 13 = 0, find the value of k and the other roots of the equation.

Firstly, we note that a 'root' is simply a solution of the equation (at least, in this case). Let's start from what we've been told: x = 1/2 is a root of the equation. Since it's a solution, let's sub it in and get rid of all the 'x's in our equation, which will leave us with an equation of only numbers and k, letting us easily find that k = 7.

Now that we have a numberical value for k, we can solve this equation - let's look again at the question. We know that x = 1/2 solves the equation, and we can easily reorganize this to make a more useful term: x - 1/2 = 0. This is now in a form that should be familiar - one of the factors that we will see if we factorized our original equation, which is exactly what we're aiming to do. Since we have one factor already, we can simply divide the original equation by it to leave us with another factor, in the form of a quadratic. This is easiest through long division. (do example of long division). The remaining quadratic should be trivial to solve, either through recognition or just plugging the coefficients into the quadratic equation. We will be then left with our original equation in the form of three factors multiplied together, and we can easily find the other roots by diving through by the other factors.