[Math] How many quadratic polynomials exist given the two zeroes? ($1$ or $\infty$)

Question

I was reading some book which had this question:

Q. The number of [quadratic] polynomials having zeros $-2$ and $5$ is:

(A) 1
(B) 2
(C) 3
(D) More than three?

Sol. (A) 1.

But according to me there should be an infinite amount of polynomials. All these polynomials have the zeroes $-2$ and $5$:

\begin{align*}
(x+2)(x-5)&=0,\\
2(x+2)(x-5)&=0,\\
3(x+2)(x-5)&=0,\\
4(x+2)(x-5)&=0,\\
5(x+2)(x-5)&=0, \text{etc}.
\end{align*}

According to me, if we are given the two zeroes of a quadratic polynomial, then we can find $\infty$ polynomials with those two zeroes. I do not know why the answer $1$ is given in the book. Maybe it is a misprint? So am I right or the book is right?

Clarification: I just wanted to ask if these polynomials are considered to be the same or different.

Answer 1

You are right, the book is mistaken (perhaps they are taking polynomials which are constant multiples of each other as equal).