The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=2 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,108).

Question

The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=2 and roots of multiplicity 1 at x=0 and x=−3. It goes through the point (5,108).

Answer 1

(x-2)^2(x)(x+3)(3/10) = 0.3x^4 -0.3x^3 - 2.4x +3.6

(5-2)^2(5)(5+3)= 9(5)(8) = 360 360x(108/360) = 108, 108/360= 3/10