The polynomial of degree 4, P(x) has a root multiplicity 2 at x=4 and roots multiplicity 1 at x=0 and x=-4 and it goes through the point (5, 18) how do you find a formula for p(x)?

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Answer 1 · 2016-10-27T05:40:12

The polynomial is #P(x)=2/5x(x-4)^2(x+4)#

If the polynomial has a root of multiplicity 2 at #x=4#, the #(x-4)^2#
is a factor

Multiplicity 1 at #x=0#, then #x# is a factor

Multiplicity 1 at #x=-4#, then #(x+4)# is a factor

So #P(x)=Ax(x-4)^2(x+4)#

As it pases through #(5,18)# so
#18=A*5*(5-4)^2*(5+4)#

So #A=18/5*1/9=2/5#

The polynomial is #P(x)=2/5x(x-4)^2(x+4)#