The polynomial of degree 4,P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity at 1 x=0 and x=-4. It goes through the point (5, 360). Find a formula for P(x).

Question

The polynomial of degree 4,P(x) has a root of multiplicity 2 at x=1  and roots of multiplicity at 1 x=0 and x=-4. It goes through the point (5, 360). Find a formula for P(x).

campbell_st · Answer

well lets look st the roots 

so is x = 1 is a root then x - 1 = 0   then (x -1) is a factor

multiplicity means that the binomial is squared

x = 0 so x is a factor

and lastly 

x = -4 so  x + 4 = 0.... and (x + 4) is a factor so your polynomial is 

$$P(x) = a[x(x +4)(x -1)^2]$$

determine the value of a, by substituting the ordered pair x = 5 P(5) = 360 

and solving for a. 

hope this helps

anonymous · Answer

I attempted , and i have a =1/2 ?

campbell_st · Answer

yep thats the value of a... 

so distribute then multiply each term by 1/2 

and you have the polynomial

anonymous · Answer

Okay im not sure if i wrote this correctly. But 1/2(x-1)^2(x)(x+4) ?

campbell_st · Answer

well thats basically it... so you have 

P(x) = 1/2[(x^2 -2x + 1)(x^2 + 4x)]

hope that helps

anonymous · Answer

Yes, it does Thank YOU !