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.