Question

Match the following columns:

Column I	Column II
(a) $2x^2-7x+5=0$	(p) Real and equal
(b) $3x^2-2\sqrt{6}x+2=0$	(q) Real, distinct and irrational
(c) $9x^2-10x+15=0$	(r) Real distinct and rational
(d) $\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0$	(s) Imaginary

Answer 1

$$\begin{gathered} \begin{array}{l}\left(\text{a}\right)2x^2-7x+5=0\\ D=b^2-4ac=49-40=9>0 \\ \mathrm{Also},D\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{perfect}\mathrm{square}.\text{Therefore, the roots are real, distinct and rational}\text{.} \\ \left(\text{b}\right)3x^2-2\sqrt{6}x+2=0 \\ \begin{array}{l}D=b^2-4ac=24-24=0\\ \text{Therefore, the roots are real and equal}\text{.}\end{array} \\ \begin{array}{l}\left(\text{c}\right)9x^2-10x+15=0\\ D=b^2-4ac=100-540=-440<0\end{array} \\ \mathrm{Therefore},\mathrm{t}\text{he roots are imaginary}\text{.} \\ \begin{array}{l}\left(\text{d}\right)\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0\\ D=b^2-4ac=8+24=32>0\end{array} \\ \begin{array}{l}\mathrm{Also},D\mathrm{is}\mathrm{not}\mathrm{a}\mathrm{perfect}\mathrm{square}.\mathrm{Therefore},\mathrm{t}\text{he roots are real, distinct and irrational}\text{.}\\ \text{So, the correct options are}\left(\text{a}\right)\text{-}\left(\text{r}\right),\left(\text{b}\right)\text{-}\left(\text{p}\right),\left(\text{c}\right)\text{-}\left(\text{s}\right)\text{and}\left(\text{d}\right)\text{-}\left(\text{q}\right).\end{array}\end{array} \end{gathered}$$