Question

Write the quadratic polynomial whose the sum and product of itszeroes are ¼, -1 respectively.​

Answer 1

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Here's your answer

If α and β are the zeroes of the polynomial p(x) then,

(x-α) and (x-β) are factors of p(x)

Hence,

p(x) = (x-α)(x-β)

p(x) = x² -(α+β)x +αβ

Here we are given that

α+β = 1/4

αβ = -1

Substituting these values in p(x)

p(x) = x² - (1/4)x + (-1)

p(x) = x² - x/4 -1

Multiplying all the terms by 4

p(x) = 4x² -x -4

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