Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, − 7, − 14 respectively

Answer 1

Let the polynomial be ax³ + bx² + cx + d and the zeroes be α, β and γ

Then, α + β + γ = `(2)/1 = (-b)/a`

αβ + βγ + γα = `(-7)/1 = c/a`

αβγ = `(-14)/1 = (-d)/a`

∴ a = 1, b = -2, c = -7 and d = 14

Hence, the polynomial is  x³ - 2x²  - 7x + 14