Question

Find a quadratic polynomial whose sum and product of zeros are 4,1​

Answer 1

The required equation is given by :

x² - ( Sum of the zeroes) x + ( Product of the Zeros) =0

⟹ x² - 4x + 1 = 0

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Answer 2

Answer:

let α and β be the zeroes of polynomial p(x).

given,

α+β=4

αβ=1

p(x)= k( x^2-(α+β)x + (αβ) )

p(x) = k(x^2-(4)x+(1))

p(x)= k( x^2-4x+1)

The polynomial whose sum and product of zeros are 4,1 is k( x^2-4x+1) where k is some integer.