Question

what is the number of polynomials having 3 and 7 as zeroes?

Answer 1

Step-by-step explanation:

There can be infinite number of polynomials with zeros - 3 and 7. We can consider another polynomial g(x) = 2 f(x), which has zeros - 3 and 7. In this way we can find F(x) = n f(x), where n is any real number and F(x) will contain zeros - 3 and 7

Answer 2

There are infinite number of polynomials having 3 and 7 as zeroes

Given : The zeroes are 3 and 7

To find : The number of polynomials

Solution :

Step 1 of 2 :

Write down the given zeroes

Here it is given that the zeroes of the polynomial are 3 and 7

Step 2 of 2 :

Find the number of polynomials

Suppose 3 and 7 are zeroes of the polynomial of multiplicity m and n respectively

Then the polynomial is of the form

$\sf {(x - 3)}^{m} {(x - 7)}^{n}$

Where m and n are natural numbers

Since m and n can be any natural numbers

So number of polynomials are infinite

Hence there are infinite number of polynomials having 3 and 7 as zeroes

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