Question

find a quadratic polynomial of a given no.and the sum and product of its zeroes respectively ‐1\4 and 1/4​

Answer 1

Answer:

This is your answer.hope it is correct.

Answer 2

Given that,

• Sum of the zeroes of a quadratic polynomial = -1/4
• Product of the zeroes of a quadratic polynomial = 1/4

As we know that,

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$\boxed{\boxed{\tt\purple{\bigstar \: quadratic \: polynomial = {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes }}}$

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Now,

$\tt:\implies \: quadratic \: polynomial = {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes$

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$\tt:\implies \: quadratic \: polynomial \: = {x}^{2} - {\large( \dfrac{ - 1}{4} )}x \: + {\large( \dfrac{1}{4} )}$

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$\tt:\implies \: quadratic \: polynomial = {x}^{2} + {\large\dfrac{1}{4}x } + {\large \dfrac{1}{4} }$

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Multiply throughout equation by 4.

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$\tt:\implies \: \boxed{\boxed{\tt\purple{quadratic \: polynomial = {4x}^{2} + x + 1 }}}\bigstar$

Hence, the quadratic polynomial is 4x² + x + 1.