The polynomial of degree 4, P(x) has a root of multiplicity 2 at x=1 and roots of multiplicity 1 at x=0 and x=-1. It goes through the point (5,192). Find a formula for P(x)

P(x) = 0.4*(x-1)(x-1)(x)(x+1)

Step-by-step explanation:

P(x) is a polynomial of degree 4, so it has 4 roots. The roots of P(x) are:

1, 1, 0, -1.

A general form for a polynomial of degree 4 is:

P(x) = a(x-x1)(x-x2)(x-x3)(x-x4)

where 'a' is a constant coefficient, and x1, x2, x3 and x4 are the roots.

So, we have that:

P(x) = a(x-1)(x-1)(x)(x+1)

We know that the polynomial goes through the point (5,192), so using the value of x=5, we have that P(x)=192. Using these values, we can find the value of 'a':

192 = a(5-1)(5-1)(5)(5+1)

192 = a*4*4*5*6

480*a = 192

a = 192/480 = 0.4

So we have that P(x) = 0.4*(x-1)(x-1)(x)(x+1)

the function makes a strait line horizontally with no x intercept but a y intercept at 9.

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