## The polynomial of degree 3 3 , P ( x ) P ( x ) , has a root of multiplicity 2 2 at x = 1 x = 1 and a root of multiplicity 1 1 at x = − 1 x =

Question

The polynomial of degree 3 3 , P ( x ) P ( x ) , has a root of multiplicity 2 2 at x = 1 x = 1 and a root of multiplicity 1 1 at x = − 1 x = – 1 . The y y -intercept is y = − 0.8 y = – 0.8 . Find a formula for P ( x ) P ( x ) . P ( x ) =

in progress 0
5 months 2021-08-27T12:36:39+00:00 1 Answers 2 views 0

## Answers ( )

A formula for P(x) is;

P(x) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8

Step-by-step explanation:

The given parameters of the polynomial are;

The degree of the polynomial = 3

The multiplicity of the root at x = 1 is 2

The multiplicity of the root at x = -1 is 1

The y-intercept is y = -0.8

Therefore, we have to find the formula for the three degree polynomial;

The factors of the three degree polynomial are (x – 1)², and (x + 1)

Multiplying the factors together, we get;

(x – 1)²×(x + 1) = x³ – x² – x + 1

f(0) = -0.8, therefore, we get;

P(x) = -0.8 × (x – 1)² × (x + 1) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8

The required polynomial is;

P(x) = -0.8·x³ + 0.8·x² + 0.8·x – 0.8