Find a polynomial of the specified degree that satisfies the given conditions. Degree 4; zeros −1, 1, 7 ; integer coefficients a

Question

1 year ago

8

nd constant term 14 f(x) =

1 answer:

kirill115 [55] · Answer 1 · 2023-12-07T05:22:05+03:00

The polynomial equation is f(x) = (x + 1)(x - 1)(x - 7)(x + 2)

<h3>How to determine the polynomial equation?</h3>

The given parameters are

The sum of multiplicities of the polynomial equation must be equal to the degree.

This means that the multiplicity of each zero is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 1)(x - 1)(x - 7)(x - a)

Recall that

Constant term = 14

This means that

P(0) = 14

So, we have

(0 + 1)(0 - 1)(0 - 7)(0 - a) = 14

Evaluate

7(0 - a) = 14

Divide by 7

0 - a = 2

So, we have

a = -2

Substitute a = -2 in P(x) = (x + 1)(x - 1)(x - 7)(x - a)

P(x) = (x + 1)(x - 1)(x - 7)(x + 2)

Rewrite as

f(x) = (x + 1)(x - 1)(x - 7)(x + 2)

Hence, the equation of the polynomial equation is f(x) = (x + 1)(x - 1)(x - 7)(x + 2)