x + Therefore, ( x – ) + = x – can be rewritten as x – x + = x – x – x + = It is of the form ax + bx + c = . Therefore, the given equation is a quadratic equation. (ii) Since x ( x + ) + = x + x + and ( x + )( x – ) = x – x + x + = x – x + = It is not of the form ax + bx + c = . Therefore, the given equation is not a quadratic equation.
(iii) Here, LHS = x ( x + ) = x + x x ( x + ) = x + can be rewritten as x + x = x + Therefore, we get x + x – = It is of the form ax + bx + c = . So, the given equation is a quadratic equation. (iv) Here, LHS = ( x + ) = x + x + x + ( x + ) = x – can be rewritten as x + x + x + = x – x + x + = or, x + x + = It is of the form ax + bx + c = . So, the given equation is a quadratic equation.
Remark : Be careful! In (ii) above, the given equation appears to be a quadratic equation, but it is not a quadratic equation. In (iv) above, the given equation appears to be a cubic equation (an equation of degree ) and not a quadratic equation. But it turns out to be a quadratic