Question

Write one quadratic polynomial that has one zero.

Answer 1

Hint: Here, write one quadratic polynomial which has both roots equal. This means write an expression which can be represented as perfect square form. Only one zero does not mean contains only one value of x or any variable but only one zero means both zeroes have the same value.

Complete step-by-step answer:
 Polynomials that have only one zero means both values of the variable are the same. This is the case of equal zeros of a quadratic equation.
Let x be the variable of a quadratic equation and both zeroes of the quadratic equation is 2, i.e., equal roots. This quadratic can written as (x – 2)(x – 2) = $ {(x - 2)^2} $ , in the quadratic polynomial if we change it as quadratic equation by equating it with 0, we get the two values of x as 2 and 2, or only 2.
In general form we can find as many quadratic polynomials as we want by replacing 2 by k where k is any value like, 1, 2, 3, … etc. All quadratic polynomials with any value of k have only one zero.
So, a quadratic polynomial that has only one zero is $ {(x - 2)^2} $ .

Note: In these types of questions, understand the things asked in question. As we know that quadratic polynomial means a polynomial with degree 2, or variable has two values either of the same value or different values. Do not confuse as if a polynomial has only one zero, then this will be a linear polynomial not a quadratic polynomial. Not only a quadratic polynomial can have only one value but a cubic polynomial can also have only one value.