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Solution :

We have <br> `3x^(2)-5x+2=0` <br> `implies" "9x^(2)-15x+6=0" "["multipling each term by 3"]` <br> `implies" "9x^(2)-15x=-6` <br> `implies" "(3x)^(2)-2xx3x xx(5)/(2)+((5)/(2))^(2)=-6+((5)/(2))^(2)" ""[""adding "((5)/(2))^(2)" on both sides""]"` <br> `implies" "(3x-(5)/(2))^(2)=(-6+(25)/(4))=((-24+25))/(4)=(1)/(4)=((1)/(2))^(2)` <br> `implies" "(3x-(5)/(2))=+-(1)/(2)" "["taking square root on both sides"]` <br> `implies" "3x-(5)/(2)=(1)/(2)" or "3x-(5)/(2)=(-1)/(2)` <br> `implies" "3x=((1)/(2)+(5)/(2))=(6)/(2)=3" or "3x=((-1)/(2)+(5)/(2))=(4)/(2)=2` <br> `implies" "3x=3" or "3x=2impliesx=1" or "x=(2)/(3).` <br> Hence, 1 and `(2)/(3)` are the roots of the given equation.