Question

a quadratic polynomial whose sum of product of zeros are 4 and - 21 respectively

Answer 1

let A and B be the zeroes of required quadratic polynomial.

since , we have given that the sum of zeroes = 4

A + B = 4

and also

given that product of zeroes= - 21

AB = - 21

so now
the required quadratic polynomial will be in the form :

x^2 - ( A + B ) x + AB = 0

x^2 - ( 4 ) x + ( - 21 ) = 0

x^2 - 4 x - 21 = 0
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option (A) is the correct answer
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Answer 2

Question: Find a quadratic polynomial whose sum and product of zeros are 4 and - 21 respectively.

General equation : x²− (α + β)x + αβ.

Given that (α + β) = 4 and αβ  = -21

Form the equation:

x²− (α + β)x + αβ

⇒ x² - 4x - 21

Answer: (A) x² - 4x - 21