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(i) Clearly, `(x^(2)-5x+3)` is a quadratic polynomial. <br> `:." "x^(2)-5x+3=0` isa quadratic equation. <br> (ii) Clearly, `(2x^(2)-3sqrt(2)x+6)` is a quadratic polynomial. <br> `:." "2x^(2)-3sqrt(2)x+6=0` is a quadratic equation. <br> (iii) `3x^(2)-2sqrt(x)+8` is not of the form `ax^(2)+bx+c=0.` <br> `:." "3x^(2)-2sqrt(x)+8=0` is not a quadratic equation. <br> (iv) `2x^(2)-3=0` is of the form `ax^(2)+bx+c=0,` where `a=2,b=0` and `C=-3`. <br> `:." "2x^(2)-3=0` is a quadratic equation. <br> (v) `x+(1)/(x)=x^(2)impliesx^(2)+1=x^(3)impliesx^(3)-x^(2)-1=0.` <br> And, `(x^(3)-x^(2)-1)` being a polynomial of degree 3, it is not quadratic. <br> Hence, `x+(1)/(x)=x^(2)` is not a quadratic equation. <br> (vi) `x^(2)+(1)/(x^(2))=(17)/(4)implies4x^(2)+4=17x^(2)implies4x^(4)-17x^(2)+4=0.` <br> C,ear,y.`4x^(4)-17x^(2)+4` is a polynomial of degree 4. <br> `:." "x^(2)+(1)/(x^(2))=(17)/(4)` is not a quadratic equation.