Question

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

Answer 1

ANSWER:

The given roots are 1/4 and -1.

Therefore, sum of the roots, S = 1/4 + (-1) = -3/4

And tghe product of the given roots, P = 1/4× -1 = - 1/4

Therefore, the required equation is x2 – Sx + p

i.e., x2 - (sum of the roots)x + product of the roots = 0

i.e., x2 - (-3/4)x – (-1/4)= 0

i.e, 2x2 +3/4x +1/4 = 0..

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Mark it as the brainliest answer....

Answer 2

Answer:

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