(a) Find the value of 'k' for which the quadratic equation 2 k x^2-40 x+25=0 has real and equal roots.

\[\begin{aligned} & 2 k x^{2}-40 x+25=0 \\ & a=2 \mathrm{k}, b=-40, c=25 \\ & \text { Q.E. has equal roots } \Rightarrow D=0 \\ & b^{2}-4 a c=0 \Rightarrow 1600-200 k=0 \\ & k=8 \end{aligned} \] Or \[x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}=\frac{-20 \pm \sqrt{400+600}}{2 \times 25} \] \[x=\frac{-20 \pm \sqrt{1000}}{50}=\frac{-20 \pm 10 \sqrt{10}}{50} \] \[x=\frac{-2 \pm \sqrt{10}}{5} ; x=\frac{-2+\sqrt{10}}{5}, \frac{-2-\sqrt{10}}{5} \]