Is x = 2/3 a root of 3x² + 7x - 6 = 0? For what value of k is x = 2 a root of kx² - 3x - 10 = 0?

Step 1. (a) $3 \times \dfrac{4}{9} + 7 \times \dfrac{2}{3} - 6 = \dfrac{4}{3} + \dfrac{14}{3} - 6 = \dfrac{18}{3} - 6 = 0$. So $\dfrac{2}{3}$ is a root.

Step 2. (b) $k \times 4 - 3 \times 2 - 10 = 0$, so $4k - 16 = 0$.

Step 3. Solve. $k = 4$. Check: $4 \times 4 - 6 - 10 = 0$.