What is the formula for P(x)?

Question

The polynomial of degree 4,  has a root of multiplicity 2 at  and roots of multiplicity 1 at  and . It goes through the point .Find a formula for .

Answer 1

x=1 x=1 x=0 x=-4

(x-1) (x-1) (x) (x=4)

(x-1)(x-1) = x^2 - 2x +1

(x)(x^2 -2x +1) = x^3 - 2x^2 + x

(x+4)(x^3 - 2x + x) = x^4 + 2x^3 -7x^2 + 4x

Replace (5,288) for (x,y)

y = a (x^4 + 2x^3 - 7x^2 + 4x)

288 = a [5^4 + 2(5)^3 - (5)^2 + 4(5)]

288 = a (720)

288/720 = a

a = 2/5

y = 2/5 (x^4 + 2x^3 - 7x^2 + 4x)

y = 2/5x^4 + 4/5x^3 - 14/5x^2 + 8/5x