Answer:
x³ + 2x² -3x +6
Step-by-step explanation:
We need to find the polynomial whose roots are ,
Say of we have zeroes as , α , β and γ , then the polynomial is ,
=> p(x) = k[ (x - α ) ( x - β) ( x - γ) ]
- where k is constant. Substituting the respective values , we have ,
=> p(x) = k [ ( x - (-2)) ( x - √3) ( x -√3)]
=> p(x) = k[ (x+2)(x² - 3)]
=> p(x) = k[ x(x² - 3) + 2(x² - 3) ]
=> p(x) = k[ x³ - 3x + 2x² - 6 ]
=> p(x) = k[ x³ + 2x² - 3x - 6 ]
Hence the cubic polynomial is x³ + 2x² - 3x + 6 .
