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JulsSmile [24]
1 year ago
8

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

nd constant term 14 f(x) =
Mathematics
1 answer:
kirill115 [55]1 year ago
6 0

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

  • Degree of polynomial = 4
  • Zeros of the polynomial = -1, 1 and 7
  • Constant term = 14

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)

Read more about polynomial at

brainly.com/question/17517586

#SPJ1

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