Question

The number of polynomials having zeroes as$-2$ and$5$ is

• A. $1$
• B. $2$
• C. $3$
• D. $morethan3$

Answer 1

The correct option is D

$morethan3$

given, the zeros of the polynomial are $-2$ and $5.$

We have to determine the number of polynomials that have zeros as $–2$ and $5.$

Sum of the zeroes $=\frac{–b}{a}$

$$\begin{gathered} –2+5=–\frac{b}{a} \\ 3=–\frac{b}{a} \end{gathered}$$

$b=–3$ and$a=1$

Product of the zeroes$=$ constant term$÷$ coefficient of $x^2$ i.e.

Product of zeroes $=\frac{c}{a}$

$$\begin{gathered} (-2)5=\frac{c}{a} \\ –10=c \end{gathered}$$

On substituting the values of$a,bandc$in the polynomial

$p\left(x\right)=a{x}^2+bx+c$

We obtain, $x^2–3x–10$

Therefore, the number of polynomials having zeros as$-2$ and $5$ is more than $3.$