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=-3. It goes through the point (5,256)

P(x) = ()x(x + 3)(x - 1)²

Step-by-step explanation:

Given - 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=-3. It goes through the point (5,256)

To find - Formula for P(x) ?

Proof -

Given that,

P(x) has a root of multiplicity 2 at x=1

So,

(x - 1)² is a factor.

Now,

Given that, there is roots of multiplicity 1 at x=0 and x=-3

So,

(x - 0) and ( x - (-3) are also factor

So,

P(x) can be written as

P(x) = Ax(x + 3)(x - 1)²           .........(1)

where A is a constant.

Now,

Given that, It goes through the point (5,256)

⇒At x = 5, P(x) = 256

So,

Put the values of x and P(x) in equation (1), we get

P(x) = Ax(x + 3)(x - 1)²

⇒256 = A(5)(5 + 3)(5 - 1)²

⇒256 = 5A(8)(4)²

⇒256 = 40A(16)

⇒256 = 640 A

⇒A = =

∴ we get

P(x) = ()x(x + 3)(x - 1)²

yo answer should be 6 if im not mistaken

step-by-step explanation:

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.