Which of the following is a quadratic equation? (i) `x^(2)+2x+1=(4-x)^(2)+3` (ii) `-2x^(2)=(5-x)(2x-(2)/(5))` (iii) `(k+1)x^(2)+(3)/(2)x=7" wherek"=-1` (iv) `x^(3)-x^(2)=(x-1)^(3)`

Which of the following is a quadratic equation? (i) `x^(2)+2x+1=(4-x)^

1.	Which of the following is a quadratic equation? (i) `x^(2)+2x+1=(4-x)^(2)+3` (ii) `-2x^(2)=(5-x)(2x-(2)/(5))` (iii) `(k+1)x^(2)+(3)/(2)x=7" wherek"=-1` (iv) `x^(3)-x^(2)=(x-1)^(3)`
Answer» (i) `x^(2)+2x+1=(4-x)+3` `impliesx^(2)+2x+1=16+x^(2)-8x+3` `implies10x-8=0` which is not in the form of `ax^(2)+bx+c,ane0` Thus, the equation is not quadratic. (ii) `-2x^(2)=(5-x)(2x-(2)/(5))` `implies-2x^(2)=10x-2-2x^(2)+(2x)/(5)` `implies50x+2x-10=0` `implies52x-10=0` which is not a quadratic equation. (iii) `(k+1)x^(2)+(3)/(2)x=7` Given k=-1 `implies(-1+1)x^(2)+(3)/(2)x=7` `implies3x-14=0` which is not a quadratic equation. (iv) `x^(3)-x^(2)=(x-1)^(3)` `impliesx^(3)-x^(2)=x^(3)-1-3x(x-1)" "[because(a-b)^(3)=a^(3)-b^(3)-3ab(a-b)]` `impliesx^(3)-x^(2)=x^(3)-1-3x^(2)+3x` `implies2x^(2)-3x+1=0` which is in the form of `ax^(2)+bx+c=0,ane0` Hence, it is a quadratic equation.