Which of the following are quadratic equations?
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
(vii) 
(viii) 
(ix) 
(x) 
(xi) 
(xii) 
(xiii) 
(xiv) 
(xv) 
A polynomial equation is a quadratic equation, if it is of the form ax2 + bx + c = 0 such that a ≠ 0
(i) 
It is a quadratic equation.
(ii) 
It is a quadratic equation.
(iii) 
⇒ x4 -5x2 + 1 = 0
It is not a quadratic equation as the highest power of x is ‘4’.
(iv) 
⇒ x2 – 3 = x3
It is not a quadratic equation.
(v) 
It is not a quadratic equation as √x is present instead of ‘x’.
(vi) 
It is not a quadratic equation as an additional √x term is present.
(vii) 
⇒ 2x2 + 2x + 6 = 0
It is a quadratic equation.
(viii) 
⇒ x2 + 1 – x = 0
It is a quadratic equation.
(ix) 
It is a quadratic equation.
(x) 
⇒ x4 + 1 + 2x2 = 3x3 + 3x + 4x2
It is not a quadratic equation.
(xi) 
⇒ 6x2 + 7x + 2 = 6x2 – 18x + 12
⇒ 25x = 10
It is not a quadratic equation.
(xii) 
⇒ x2 + 1 = x3
It is not a quadratic equation.
(xiii) 
⇒ 16x2 – 3 = 10x2 + 19x – 15
⇒ 6x2 – 19x + 12 = 0
It is a quadratic equation.
(xiv) 
⇒ x3 + 8 + 6x2 + 12x = x3 – 4
⇒ 6x2 + 12x + 12 = 0
It is a quadratic equation.
(xv) 
⇒ x2 + x + 8 = x2 – 4
⇒ x = - 12
It is not a quadratic equation.