Question

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

• A. $1$
• B. $2$
• C. $3$
• D. more than $3$

Answer 1

The correct option is D

more than $3$

Let the zeroes of the polynomial be α = -2 and $\beta =5.$

The general form of polynomial with $\alpha$ and $\beta$ as the zeroes is given by:

$k[x^2–(\alpha +\beta )x+\alpha \beta ],k$is any real number

$=k[x^2–(-2+5)x+(-2)(5\left)\right]$

$=k(x^2–3x–10)$

Hence, more than $3$ polynomials can have the zeroes $-2$ and $5.$