The polynomial P(x) of degree 4 has, a root of multiplicity 2 at x=4, a root of multiplicity 1 at x=0 and at x=-2. It goes through the point (5,24.5)

Wotzdorfg

Wotzdorfg

Answered question

2021-09-07

The polynomial P(x) of degree 4 has
a root of multiplicity 2 at x=4
a root of multiplicity 1 at x=0 and at x=-2
It goes through the point (5,24.5)
Find a formula for P(x)

Answer & Explanation

Daphne Broadhurst

Daphne Broadhurst

Skilled2021-09-08Added 109 answers

Given that the polynomial P(x),
The polynomials P(x) is a root of multiplicity 2 at x=4
So the factor of polynomials is (x4)2
The polynomials P(x) is a root of multiplicity 1 at x=0
So the factor of polynomials is "x"
The polynomials P(x) is a root of multiplicity 1 at x=-2
So the factor of polynomials is: (x+2)
Therefore the polynomials P(x) will be,
P(x)=A(x4)2(x0)(x+2)
P(x)=Ax(x4)2(x+2)
Where A is constant
The given polynomials P (x) goes through the points (5, 24.5) then the points is satisfied the equation then,
P(5)=A5(54)2(5+2)
24.5=A(5)(1)7
24.5=35A
A=24.535
=24535×10
A=710
Substitute A=710 in equation then,
P(x)=710x(x4)2(x+2)
Hence the polynomial of degree 4 is P(x)=710(x4)2x(x+2)

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