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

y=x(x-2)^2(x+3) = (x^2-4x+4)(x^2+3x) =x^4-x^3-8x^2+12x

let y=108 and x = 5

108=625-125-200+60= 360 which could be changed to 108 by multiplying by 108/360 =3/10

y = (3/10)(x^4 -x^3 -8x^2 +12x)

y=3x^4/10 -3x^3/10-4x^2/5 +18x/5

y = 0.3x^4 - 0.3x^3 -0.8x^2 + 3.6x