Question

find the quadratic polynomial the sum and product of whose zeroes are -1/4 and 1/4 respectively

Answer 1

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Answer 2

Answer:

The required quadratic equation or polynomial is 4x^2 + x + 1.

Step-by-step explanation:

Given : Sum of the zeroes       = (-1/4)

            Product of the zeroes = 1/4

We know that, if we have sum and product of zeroes then, we can find the quadratic equation by putting the value of sum and product of zeroes.

∴,

p(x) = x^2 - (Sum of zeroes)x + (Product of zeroes)

p(x) = x^2 - (-1/4)x + (1/4) = 0

p(x) = x^2 + x/4 + 1/4 = 0

p(x) = 4x^2 + x + 1/4 = 0

p(x) = 4x^2 + x + 1 = 0

Hence, the required quadratic equation or polynomial is 4x^2 + x + 1.

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