Question

find quad. polynomial whose product and sum of zeroes are 1 and 5/2

Answer 1

Answer:

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Answer 2

Given :  Product and sum of zeroes of a polynomial are 1 and 5/2 respectively

To find : polynomial

Solution:

polynomial

= x²  - (sum of zeroes)x  + product of zeroes

= x²  - 5x/2  + 1

=> 2x² - 5x + 2

Another Way

let say zeroes are α , β

Product of Zeroes = 1

=> α , β = 1

sum of zeroes are 1

=> α +  β = 5/2

polynomial will be

(x - α )(x -  β)

= x² - αx - βx  + αβ

= x²  -(α + β)x + αβ

= x² - (5/2)x  + 1

=> 2x²  - 5x  + 2

2x²  - 5x  + 2  is the polynomial whose product and sum of zeroes are 1 and 5/2 respectively

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