Answer: [tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0
Step-by-step explanation:
Since the zeros of the polynomials are -3 , 4 and 1 , then the equation will be in the form:
(x+3)(x-4)(x-1) = 0
Expanding (x+3)(x-4) , we have
[tex]x^{2}[/tex] - 4x + 3x - 12
⇒[tex]x^{2}[/tex] -x - 12
combining with (x-1) , we have
([tex]x^{2}[/tex] -x - 12) ( x -1 ) = 0
expanding , we have :
[tex]x^{3}[/tex] - [tex]x^{2}[/tex]-[tex]x^{2}[/tex] + x - 12x + 12 = 0
⇒[tex]x^{3}[/tex] - 2[tex]x^{2}[/tex] - 11x + 12 = 0
