The number of polynomials having zeros as 2and 5 is


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

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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 :


P(x)=a(x-c)^n(x-d)^m

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


P(x)=a(x+2)^n(x-5)^m

 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.


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