Question

The number of polynomials having zeroes as - 2and 5​

Answer 1

GIVEN :

The polynomial whose zeroes are -2 and 5.

TO FIND :

The number of polynomials.

SOLUTION :

Given that the zeroes are -2 and 5

Let P(x) be the polynomial whose zeroes are -2 and 5

Polynomial having zeroes as c and d is of the form :

[tex] P(x)=a(x-c)^n(x-d)^m[/tex]

Polynomial having zeroes as -2 and 5 can be written as

[tex] P(x)=a(x+2)^n(x-5)^m[/tex]

 where n and m can assign any value from 1, 2, 3,...

⇒ there must be infinitely many  polynomials having zeroes as -2 and 5.

∴ the number of polynomials is > 3.