Question

write a quadratic polynomial whose sum of zeros is-1/4
and product of zeros is √5​

Answer 1

Answer:

The sum of its zeros (α+β) = -1/4

product of its zeroes (αβ) =√5

now, The required polynomial is = k[x²-(α+β)x +αβ]

=k[x²-(-1/4x) + √5]

= k [ x ² + 1/4x + √5 ]

= k [ 4x ²+ x +4√5 /4]

= k/4 [ 4x² + x + 4√5]

so the polynomial is 4x²+ x + 4√5