Question

find a cubic polynomial whose zeros are - 2, 1/2, 1​

Answer 1

polynomial = x³-(sum of zeroes)x²+(product,taking two at time)x +(product)

=x³-(-2+1+1/2)x²+(-1x1/2x-2)x-(-2x1/2x1)

=x³-x²/2+x+1

$= \frac{1}{2} ( {2x}^{3} - {x}^{2} + 2x + 2)$