Problema Solution
the polynomial of degree 4. p(x) has a root of multiplicity 2 at x=4 and roots of multiplicity 1 at x=0 and x=2 it goes through the point (5,14) find a formula for p(x)
Answer provided by our tutors
p(x) = C(x - 4)^2 * x * (x - 2), where C is constant
p(x) goes trough (5, 14) means
p(5) = 14 or
C(5 - 4)^2 * 5 * (5 - 2) = 14
C*15 = 14
C = 14/15
now we can write:
p(x) = (14/15)(x - 4)^2 * x * (x - 2)
p(x) = (14/15)(x^4 - 10x^3 + 32x^2 - 32x)
p(x) = (14/15)x^4 - (28/3)x^3 + (448/15)x^2 - (448/15)x