Question

If 3, 7 are the zeros of a polynomial , then polynomial is​

Answer 1

Solution :-

We have,

→ Sum of zeros of polynomial = 3 + 7 = 10

→ Product of polynomial = 3 * 7 = 21 .

we know that, a polynomial with sum and product of its zeroes can be written as ,

→ x² - (sum of zeroes) * x + product of zeroes

→ x² - 10x + 21 .

therefore, the required polynomial is equal to x² - 10x + 21 .

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Answer 2

Given :  3, 7 are the zeros of a polynomial

To Find : polynomial

Solution:

P(x) -polynomial having zeroes a and b can be represented by

P(x) = k(x - a)(x - b)  where k is non zero real number

3, 7 are the zeros of a polynomial

a = 3

b = 7

p(x) = k(x - 3)(x - 7)

=> p(x) = k( x² - 10x + 21)

=> p(x) = kx²  - 10kx + 21k

p(x) = k( x² - 10x + 21)  is the required polynomial

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