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(D) quadratic polynomial is given by the formula $p(x) = k[x^{2} - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero real c

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$k(4x^{2} + x + 1)$

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(D) quadratic polynomial is given by the formula $p(x) = k[x^{2} - (	ext{sum of zeros})x + (	ext{product of zeros})]$,where $k$ is a non-zero real constant.Given that the sum of the zeros $= -\frac{1}{4}$ and the product of the zeros $= \frac{1}{4}$.Substituting these values into the formula:$p(x) = k[x^{2} - (-\frac{1}{4})x + \frac{1}{4}]$$p(x) = k[x^{2} + \frac{1}{4}x + \frac{1}{4}]$To simplify,we can take $k = 4$ (or any multiple of $4$):$p(x) = 4[x^{2} + \frac{1}{4}x + \frac{1}{4}]$$p(x) = 4x^{2} + x + 1$Thus,the general form is $k(4x^{2} + x + 1)$.

Obtain a quadratic polynomial with the following conditions:
The sum of the zeros $= -\frac{1}{4}$;
The product of the zeros $= \frac{1}{4}$.

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Obtain a quadratic polynomial with the following conditions:The sum of the zeros $= -\frac{1}{4}$;The product of the zeros $= \frac{1}{4}$.