Question

Consider the graph of the sixth degree polynomial f. Replace the values b, c and d to write function f.

f(x) = (x-b)(x-c)^2(x-d)^3

​

Answer 1

Answer:

f(x) = (x - 2)(x + 1)²(x - 4)³

Step-by-step explanation:

Multiplicity of a polynomial:

1). If the multiplicity is odd, the graph will cross the x-axis at that zero.

2). If the multiplicity is even, the graph will touch the x-axis at that zero.

Since the given graph is just touching the x-axis at x = -1 multiplicity for the zero (at x = -1) will be even.

Similarly, graph is crossing the x-axis at x = 2 and x = 4, multiplicity for the zero will be odd.

So, the function will be,

f(x) = (x - 2)(x + 1)²(x - 4)³