Answer:
A, B, D
Step-by-step explanation:
You want the zeros of the polynomial function f(x) = x⁴ −4x³ −22x² +4x +21.
A graphing calculator provides the zeros quickly and easily. They are ...
-3 . . . . choice A
-1 . . . . choice B
1 . . . . not a choice
7 . . . . choice D
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Additional comment
There is a zero at x=0 if and only if the polynomial has no constant term (x is a factor of every term). That is not the case here.
The zeros of the polynomial function f(x) = x⁴ − 4x³ − 22x² + 4x + 21 are the solutions to the equation when set to zero. By testing the options provided using synthetic division or substitution, we find that the correct zero from the given options is 7. Option d) is correct answer.
The student asked for help to find the zeros of the polynomial function f(x) = x⁴ − 4x³ − 22x² + 4x + 21. The zeros of a polynomial are the values of x that make the function equal to zero. In this polynomial, we can attempt to find zeros through a number of methods such as factoring, graphing, or applying the Rational Root Theorem.
To apply the Rational Root Theorem, we list all potential rational zeros as ± factors of the constant term over factors of the leading coefficient. In this case, the constant term is 21, and the factors of 21 are 1, 3, 7, and 21. The leading coefficient is 1, which has just one factor: 1 itself.
The potential rational zeros are therefore ± 1, ± 3, ± 7, and ± 21. By using synthetic division or direct substitution, one can test these potential zeros to see which ones are actual zeros of the polynomial. After testing the options given: a) -3, b) -1, c) 0, and d) 7, only option d) 7 is found to be a root of the polynomial, as f(7)=0.
