Question

The graph below is a polynomial function in the form f(x)=(x−a)^2(x−b)(x−c). Find suitable unique real numbers a, b, and c that describe the graph.

Answer 1

Answer:

The suitable unique real numbers $a$, $b$ and $c$ of the function in the form $f(x) = (x-a)^{2}\cdot (x-b)\cdot (x-c)$ are -1, 1 and 3, respectively.

Step-by-step explanation:

The form given of the polynomial contains the points ($a$, $b$, $c$) where $f(x) = 0$. Then, the following conditions must be observed to determine the possible polynomial:

$(x-a)^{2} = 0$ (1)

$x-b = 0$ (2)

$x-c = 0$ (3)

From (1) we know that it is second polynomial with an unique solution at its vertex. Hence, the value for $a$ must be -1. Lastly, the remaining roots of the polynomial are supposed to be $b = 1$ and $c = 3$.

The suitable unique real numbers $a$, $b$ and $c$ of the polynomial function in the form $f(x) = (x-a)^{2}\cdot (x-b)\cdot (x-c)$ are -1, 1 and 3, respectively. We proceed to attach an image as complementary proof of the results found in direct inspection.

Answer 2

The suitable unique real numbers a, b and C that describe the given graph are;

a = -1

b = 1

c = 3

We are given the polynomial function of the graph as;

f(x) = (x - a)²(x - b)(x - c)

Now, what this means is that the factors of the polynomial are;

(x - a)², (x - b) and (x - c).

Now, the solution to the polynomial will be the values of x when the factors equal zero.

This means that a, b and c are solutions of the polynomial function. This means a, b and C are the x-intercepts.

Looking at the graph, the x intercepts are;

-1, 1 and 3.

Thus;

a = -1

b = 1

c = 3

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