Question

The number of polynomial 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 $3$

Here we have to find the number of polynomial having zeroes as $-2$ and $5$

Let the zeroes of the polynomial be $\alpha =-2$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
$=k[x^2–(-2+5)x+(-2\left)\right(5\left)\right]=k(x^2-3x–10)$
Thus, more than $3$ polynomials can have the zeroes $-2$and $5.$

Hence, option D is correct.