Question

If A={x/6x^ 2 +x-15=0} ; B={x/2x^ 2 -5x-3=0} ; C= {x/2x^ 2 -x-3= ; then find i) (A union B union C) ii)(A intersection B intersection C)

Answer 1

$\textbf{Given:}$

$A=\{x/6x^ 2 +x-15=0\}$

$B=\{x/2x^ 2 -5x-3=0\}$

$C= \{x/2x^ 2 -x-3=0\}$

$A=\{x/6x^ 2 +x-15=0\}$

$A=\{x/(3x+5)(2x-3)=0\}$

$A=\{x/x=\frac{-5}{3},\frac{3}{2}\}$

$B=\{x/2x^ 2 -5x-3=0\}$

$B=\{x/(x-3)(2x+1)=0\}$

$B=\{x/3,\frac{-1}{2}\}$

$C= \{x/2x^ 2 -x-3=0\}$

$C= \{x/(2x-3)(x+1)=0\}$

$C= \{x/x=\frac{3}{2},-1\}$

$\text{We have}$

$\bf\;A=\{\frac{-5}{3},\frac{3}{2}\}$

$\bf\;B=\{3,\frac{-1}{2}\}$

$\bf\;C= \{\frac{3}{2},-1\}$

$(i)$

$A{\cup}B{\cup}C$

$=\{\frac{-5}{3},\;-1,\;\frac{-1}{2},\;\frac{3}{2},\;3\}$

$(ii)$

$A{\cap}B{\cap}C=\{\}\;$ $\;(\because\text{no element is common to all the sets})$