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)

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²

it would be 4 over -2 divided by -1 over 3.

if you want a solution it would be 4

you flip it so it would be 4/-2 divided by 3/-1 then it would be 12/3 and you would simplify it to 4