Answer:
Step-by-step explanation:
A graphing calculator makes finding or verifying the zeros of a polynomial function as simple as typing the function into the input box.
The attachment shows the function zeros to be x ∈ {-2, 3, 7}, as required.
The leading coefficient of this odd-degree polynomial is positive, so the value of f(x) tends toward infinity of the same sign as x when the magnitude of x tends toward infinity.
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Additional comment
The function is entered in the graphing calculator input box in "Horner form," which is also a convenient form for hand-evaluation of the function.
We know the x^2 coefficient is the opposite of the sum of the zeros:
-(7 +(-2) +3) = -8 . . . . x^2 coefficient
And we know the constant is the opposite of the product of the zeros:
-(7)(-2)(3) = 42 . . . . . constant
These checks lend further confidence that the zeros are those given.
(The constant is the opposite of the product of zeros only for odd-degree polynomials. For even-degree polynomials. the constant is the product of zeros.)
