Question

If the equation has equal roots, then k = ?
(a) 2 or 0
(b) −2 or 0
(c) 2 or −2
(d) 0 only

Answer 1

(c) 2 or −2
$$\begin{gathered} \mathrm{It}\mathrm{is}\mathrm{given}\mathrm{that}\mathrm{the\; roots\; of\; the\; equation}(9x^2\text{+}6kx+4=0)\text{are equal.} \\ \therefore (b^2-4ac)=0 \\ \Rightarrow {\left(6k\right)}^2-4\times 9\times 4=0 \\ \Rightarrow 36k^2=144 \\ \Rightarrow k^2=4 \\ \Rightarrow k=\pm 2 \end{gathered}$$