Question

for what value of k will 7/3 be a root of 3x2-13k-k=0
(A)14 (B) 3/7 (C) -7/2 (D) -14

Answer 1

$$\begin{gathered} \mathrm{Given},\frac{7}{3}\mathrm{be}\mathrm{a}\mathrm{root}\mathrm{of}3{\mathrm{x}}^2-13\mathrm{x}-\mathrm{k}=0.\mathrm{So}, \\ 3{\left(\frac{7}{3}\right)}^2-13\left(\frac{7}{3}\right)-\mathrm{k}=0 \\ \Rightarrow \frac{49}{3}-\frac{51}{3}=\mathrm{k} \\ \Rightarrow \frac{49-51}{3}=\mathrm{k} \\ \Rightarrow \mathbf{k}\mathbf{=}\mathbf{-}\frac{\mathbf{2}}{\mathbf{3}} \end{gathered}$$