Enter the number of complex zeros for the polynomial function in the box.
2 answers:
F(x) = x³ - 96x² + 400
Apply Descartes' Rule of Signs.
The number of changes in sign is 2, so there are
(i) either 2 positive real zeros, or
(ii) a pair of conjugate complex zeros.
f(-x) = -x³ - 96x² + 400
The number of changes in sign is 1.
There is one negative real zero.
To determine whether there are 2 real zeros, we should test for zero crossings.
x f(x)
---- ----------
-4 -1200
-2 8
0 400
2 24
4 -1072
There are 2 zero crossings, therefore there are 2 real zeros and no complex zeros.
The graph of f(x) confirms the analysis.
Answer: 0
Apply Descartes' Rule of Signs.
The number of changes in sign is 2, so there are
(i) either 2 positive real zeros, or
(ii) a pair of conjugate complex zeros.
f(-x) = -x³ - 96x² + 400
The number of changes in sign is 1.
There is one negative real zero.
To determine whether there are 2 real zeros, we should test for zero crossings.
x f(x)
---- ----------
-4 -1200
-2 8
0 400
2 24
4 -1072
There are 2 zero crossings, therefore there are 2 real zeros and no complex zeros.
The graph of f(x) confirms the analysis.
Answer: 0
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