Question

The number of polynomials having zeros as -2 and 5 is
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Answer 1

Answer:

ANSWER

Polynomial having zereos as 2 and 5 is of the form:

P(x)=a(x−2)

n

(x−5)

m

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

Therefore, there can be infinite polynomials having zereos as 2 and 5.

Hence, the number of polynomials is >3.

Answer 2

The number of polynomials having zeros as -2 and 5 is

The required quadratic polynomial is

$(x-(-2))(x-5)$

   $=(x+2)(x-5)\\=x(x+2)+2(x-5)\\=x^2-5x+2x-10\\=x^2-3x-10$

• But, we can multiply any constant to this polynomials,

and that polynomial would have the same zeros.

• There are infinite such polynomials
• So the answer is more than 3.

Infinite polynomial

• f(x)=sinx cannot be since a polynomial  has only finitely many roots and the sine function has infinitely many roots.
• A standard technique in the 18th century was to write such functions as an " infinite polynomial ", what we typically refer to a as power series.