The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=3 and roots of multiplicity 1 at x=0 and x=-3. It goes through the point (5,112). How do you find a formula for P(x)?

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Answer 1 · 2017-09-26T21:11:32

A polynomial of degree 4 will have the root form:

#y=k(x-r_1)(x-r_2)(x-r_3)(x-r_4)#

Substitute in the values for the roots and then use the point to find the value of k.

Substitute in the values for the roots:

#y=k(x-0)(x-3)(x-3)(x-(-3))#

Use the point #(5,112)# to find the value of k:

#112=k(5-0)(5-3)(5-3)(5-(-3))#

#112=k(5)(2)(2)(8)#

#k = 112/((5)(2)(2)(8))#

#k = 7/10#

The root from of the polynomial is:

#y=7/10(x-0)(x-3)(x-3)(x-(-3))#