Question

quadratic polynomial whose sum of zero is -1 / 4 and product of zero is 1 /4​

Answer 1

Answer:

this is a second way to solve the question

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Answer 2

$\displaystyle \sf The \: quadratic \: polynomial \: is \: \: \: {x}^{2} + \frac{x}{4} + \frac{1}{4}$

Given :

For a quadratic polynomial whose sum of zeroes is - 1/4 and product of zeroes is 1/4

To find :

The quadratic polynomial

Concept :

If the Sum of zeroes and Product of the zeroes of a quadratic polynomial is given then the quadratic polynomial is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

Solution :

Step 1 of 2 :

Write down sum of zeroes and product of the zeroes of the quadratic polynomial

For the given Quadratic polynomial

Sum of zeroes = - 1/4

Product of the zeroes = 1/4

Step 2 of 2 :

Find the quadratic polynomial

The required quadratic polynomial

$\sf{ = {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes }$

$\displaystyle \sf = {x}^{2} - \bigg( - \frac{1}{4} \bigg)x + \bigg( \frac{1}{4} \bigg)$

$\displaystyle \sf = {x}^{2} + \frac{x}{4} + \frac{1}{4}$

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