Question

For what real values of k, the equation $9x^2+8kx+16=0$ has real and equal roots?
(a) k = 2 or −2
(b) k = 3 or −3
(c) $k=\frac{4}{3}\mathrm{or}\frac{-4}{3}$
(d) None of these

Answer 1

(b) k = 3 or −3

$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the}\mathrm{roots}\mathrm{of}\mathrm{the}\mathrm{equation}(9x^2+8kx+16=0)\text{are real and equal.} \\ \therefore D=0 \\ \Rightarrow (b^2-4ac)=0 \\ \Rightarrow 64k^2-4\times 9\times 16=0 \\ \Rightarrow 64k^2-576=0 \\ \Rightarrow k^2=9 \\ \Rightarrow k=3\text{or}-3 \end{gathered}$$