Question

find a quadratic polynomial whose sum and product of zeroes are 1/4 -1​

Answer 1

Answer:

Answer is

${x}^{2} - \frac{1}{4} x \: - 1$

Step-by-step explanation:

Let the roots be α and β

Then given in que

α + β = 1/4

αβ. = -1

We know that the form of quadratic polynomial when there sum and product of roots is given is

${x}^{2} - ( \alpha + \beta )x + \alpha \beta$

So here our quadratic polynomial will be

${x}^{2} - \frac{1}{4} x \: + ( - 1)$

${x}^{2} - \frac{1}{4} x \: - 1$

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Answer 2

Answer:

$Given, \: Sum \: of \: zeroes \: = 1/4</p><p> \\ and \: product \: of \: zeros = \: -1 \\ </p><p>Then, \: the \: quadratic \: polynomial \\ = k \: [ {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes ] \\ k( {x}^{2} - ( \frac{1}{4} )x - 1 \\ = k( {x}^{2} - \frac{x}{4} - 1) \\ = k( \frac{4 {x}^{2} - x - 4 }{4 } ) \\ If \: k = 4, \: then \: the \: required \: quadratic \: polynomial \: is \\⇒ \: 4 {x}^{2} - x - 4</p><p>$