I write the quadratic polynomials from the following polynomials by understanding it.

i. x² – 7x + 2

ii. 7x⁵ – x(x + 2)

iii. 2x (x+5) + 1

iv. 2x – 1

(i) The given equation is x² – 7x + 2

This equation is of the form ax² + bx + c = 0 where a,b,c are real numbers as a = 1 which is not equal to 0,b = -7 and c = 2.

Hence, this equation is a quadratic equation.

(ii) The given equation is 7x⁵ – x(x + 2)

This equation is not of the form ax² + bx + c = 0 where a,b,c are real numbers as the highest degree of x in the equation is 5.

Hence, this equation is not a quadratic equation.

(iii) The given equation is 2x (x+5) + 1

Therefore, this equation is of the form ax² + bx + c = 0 where a,b,c are real numbers as a = 2 which is not equal to 0,b = 10 and c = 1.

Also the highest degree of x in the equation is 2.

Hence, this equation is a quadratic equation.

(iv) The given equation is 2x-1

This is a linear equation with highest degree of x is 1.

This is of the form ax² + bx + c = 0 where a,b,c are real numbers but here a = 0 which does not satisfy the condition of quadratic equations.

Hence, this equation is not a quadratic equation.