Question

Find a quadratic polynomial, the sum and product of whose zeroes are given as 1/4 and -1

respectively

Answer 1

Hey

Here is your answer,

Sum of zeroes = 1/4
Product of zeroes = -1

Quadratic polynomial = x^2 - (Sum of zeroes)x + product of zeroes

=x^2 - (1/4)x -1
=4x^2-x -4

Hope it helps you!

Answer 2

Answer:

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