1.

Which of the following are quadratic equations? `(i) x^(2)-5x+3=0`(ii) `2x^(2)-3sqrt(2)x+6=0` (iii) `3x^(2)-2sqrtx+8=0`(iv) `2x^(2)-3=0` (v) `x+(1)/(x)=x^(2)`(vi) `x^(2)+(1)/(x^(2))=4(1)/(4)`

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


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