Question

Which of the following polynomial is a quadratic polynomial: (i)x²-7x+2 (ii) 7x²-x(x+2) (iii) 2x (x+5)+1 (iv) 2x-1

Answer 1

The general form of a quadratic ploynomial is given by,

`ax^2+bx+c`

Here, a, b and c are real numbers and a not equal to zero.

The highest degree of a quadratic polynomial is 2.

Option (i)

The highest degree of the given polynomial is 2. Therefore, the polynomial is quadratic.

Option (ii)

`\begin{gathered} 7x^2-x(x+2)=7x^2-x^2-2x \\ =6x^2-2x \end{gathered}`

The highest degree of the polynomial is 2. Therefore, the polynomial is quadratic.

Option (iii)

`2x(x+5)+1=2x^2+10x+1`

The highest degree of the polynomial is 2. Therefore, the polynomial is quadratic.

Option (iv)

2x-1

The highest degree of the polynomial is 1. Therefore, the polynomial is not quadratic.

Hence, options (i), (ii) and (iii) are correct.