Question

Find a cubic polynomial with the sum, sum of the product of its zeroes taken two at a time, and product of its zeroes as 2,−5,−11 respectively, then the cubic polynomial is

Answer 1

Answer:

2×2+47(-57=08)÷1696+57-579

Answer 2

Answer:

SOLUTION

Let the polynomial be ax3 + bx2 + cx + d and the zeroes be α, β and γ Then, α + β + γ = -(-2)/1 = 2 = -b/a αβ + βγ + γα = -5 = -5/1 = c/a αβγ = -11 = -11/1 = -d/a∴ a = 1, b = -2, c = -5 and d = 11 So, one cubic polynomial which satisfy the given conditions will be x3 - 2x2  - 5x + 11