Question

If the equation $4x^2-3kx+1=0$ has equal roots, then k = ?
(a) $\pm \frac{2}{3}$
(b) $\pm \frac{1}{3}$
(c) $\pm \frac{3}{4}$
(d) $\pm \frac{4}{3}$

Answer 1

(d) $\pm \frac{4}{3}$

$$\begin{gathered} \text{It is given that the roots of the equation (4}{x}^2-3kx+1=0)\text{are equal}\text{.} \\ \therefore (b^2-4ac)=0 \\ \Rightarrow {\left(3k\right)}^2-4\times 4\times 1=0 \\ \Rightarrow 9k^2=16 \\ \Rightarrow k^2=\frac{16}{9} \\ \Rightarrow k=\pm \frac{4}{3} \end{gathered}$$