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

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 = -7 = -7/1 = c/a αβγ = -14 = -14/1 = -d/a∴ a = 1, b = -2, c = -7 and d = 14 So, one cubic polynomial which satisfy the given conditions will be x3 - 2x2  - 7x + 14

Answer 2

A+B+C=2=-b/a
AB+BC+CA=-7=c/a
A×B×C=-14=-d/a
FROM ABOVE
a=1
b=-2
c=-7
ax3+bx2+cx+d
1x3-2x2-7x+14