Answer:
[tex]x^{4}-2x^{3}-11x^{2}+12x+36[/tex]
Step-by-step explanation:
The polynomial which have four roots that means zero roots of this polynomial will be (x -2), (x -2), (x -3) and (x -3)
So the polynomial will be (x + 2)(x + 2)(x - 3)(x - 3)
= (x + 2)²(x - 3)²
= (x² + 4x + 4)(x² + 9 - 6x)
= [tex]x^{4}+4x^{3}+4x^{2}+9x^{2}+36x +36-6x^{3}-24x^{2}-24x[/tex]
= [tex]x^{4}-2x^{3}-11x^{2}+12x+36[/tex]
Therefore, the polynomial will be ([tex]x^{4}-2x^{3}-11x^{2}+12x+36[/tex])
