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)
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