Which of the following equation is quadratic?

(1) $x+\frac{3}{x}=x^2$ 

⇒$\frac{x^2+3}{x}=x^2$

⇒ x²+ 3 = x³ 

⇒ x³− x²− 3 = 0 

Here, the highest power of the variable is 3.  

Thus, the given equation is a cubic equation and not quadratic. 

(2) 3x²− 4x+ 2 = 3x²− 2x+ 4 

⇒ 3x²− 4x+ 2 − 3x²+ 2x− 4 = 0 

⇒ −4x+ 2x+ 2 − 4 = 0 

⇒ −2x − 2 = 0 

⇒ x + 1 = 0 

Here, the highest power of the variable is 1. 

Thus, the given equation is a linear equation and not a quadratic equation. 

(3) x³ + x² = x(x²+ 2) − 1 

⇒ x³+ x² = x³+ 2x− 1 

⇒ x³+ x² − x³ − 2x+ 1 = 0 

⇒ x² − 2x+ 1 = 0 

This equation is now of the form ax²+ bx+ c= 0 

Thus, the given equation is a quadratic equation. 

(4)  $\begin{array}{c}(x+2)(x-1)=x^2-2x-3\\ \Rightarrow x^2+x-2=x^2-2x-3\\ \Rightarrow 3x+1=0\end{array}$

Here, the highest power of the variable is 1. 

Thus, the given equation is a linear equation and not a quadratic equation.