Find a quadratic polynomial, the sum and
product of whose zeros are 1/4 and -1/8 ? respectively?
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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.
I hope it helps you.
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