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ALGEBRA II 6.7 THE FUNDAMENTAL THEOREM OF ALGEBRA
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THE FUNDAMENTAL THEOREM OF ALGEBRA
If f ( x) is a polynomial of degree n where n  0, then the equation f ( x)  0
has at least one root in the set of complex numbers.
Find the Number of Solutions and Zeros
1) x3  3x 2  16 x  48  0
Using Zeros to Write Polynomial Functions
2) Write a polynomial function f of least degree that has real coefficients, a leading coefficient of
1, with -2, 3, and 5 as zeros.
3) Write a polynomial function f of least degree that has real coefficients, a leading coefficient of
1, with -4 and 3 – i as zeros.
ALGEBRA II 6.7 THE FUNDAMENTAL THEOREM OF ALGEBRA
Approximating Real Zeros
4) Approximate the real zeros of f ( x)  x 4  2 x3  x 2  2 x  2  0 .
5) Approximate the real zeros of f ( x)  x3  4 x 2  5x  14  0 .
Approximating Real Life Zeros
6) For one group of people it was found that a person’s score S on the Harvard Step Test was
related to his or her amount of hemoglobin x (in grams per 100 milliliters of blood) by the
following model:
S  0.015 x3  0.6 x 2  2.4 x  19  0
The normal range of hemoglobin is 12 – 18 grams per 100 milliliters of blood.
Approximate the amount of hemoglobin for a person who scored 75.
7) For the 25 years that a grocery store has been open, its annual revenue R (in millions of dollars)
can be modeled by
1
R
 t 4  12t 3  77t 2  600t  13, 650
10, 000
where t is the number of years the store has been open. In what year(s) was the revenue
$1.5 million?
PUZZLER
On a scale, 2 green balls and 1 red ball balance 2 yellow balls. Three red balls balance 4 yellow balls.
How many green balls will balance 1 red ball?