Question

Find a cubic polynomial with the sum, sum of the product of its zeros taken two at a time, and the product of its zeros as 5, -2 and -24 respectively.

Answer 1

Any cubic polynomial is of the form $a{x}^3+b{x}^2+cx+d$

$=x^3–\left(sumofthezeroes\right)x^2+\left(sumoftheproductsofitszeroes\right)x–\left(productofthezeroes\right)$

$=x^3-\left(5\right)x^2+(-2)x-(-24)$

$=x^3-5x^2-2x+24$