Question

find the quadratic polynomials sum and product of whose. zeroes are 1/4 and -1 respectively​

Answer 1

Answer:

4x2-x-4

Step-by-step explanation:

sum of roots= 1/4

product of roots=-1

The form of quadratic polynomial =constant(x2-x(sum of the roots)+product of the roots)

:.constant(x2-x(1/4)+(-1))

=constant(4x2-x-4/4)

considering the constant as 4

:. Our required quadratic polynomial= 4x2-x-4

Remember the form of quadratic polynomial is x2-x (sum of the roots) + product of the roots

Answer 2

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