Finding a Polynomial Function In Exercises 71 − 74 , find a cubic polynomial function f with real coefficients that has the given complex zeros and x -intercept. (There are many correct answers.) Complex Zeros x -Intercept x = − 1 ± 3 i ( − 4 , 0 )
Finding a Polynomial Function In Exercises 71 − 74 , find a cubic polynomial function f with real coefficients that has the given complex zeros and x -intercept. (There are many correct answers.) Complex Zeros x -Intercept x = − 1 ± 3 i ( − 4 , 0 )
Solution Summary: The author calculates the polynomial function of degree 3 with the zeroes -1pm sqrt
Finding a Polynomial Function In Exercises
71
−
74
, find a cubic polynomial function f with real coefficients that has the given complex zeros and
x
-intercept. (There are many correct answers.)
Complex Zeros
x
-Intercept
x
=
−
1
±
3
i
(
−
4
,
0
)
Combination of a real number and an imaginary number. They are numbers of the form a + b , where a and b are real numbers and i is an imaginary unit. Complex numbers are an extended idea of one-dimensional number line to two-dimensional complex plane.
College Algebra - HW #11, Solving polynomials
Real and Complex Zeros of a Polynomial Function In
Exercises 9-12, confirm that the function has the indicated
zeros.
9. f(x) = x² + 25; -5i, 5i
10. f(x) = x² + 2; -√2i, √2i
11. f(x) = x³ + 9x; 0, -3i, 3i
12. f(x) = x³ + 49x; 0, -7i, 7i
Finding a Polynomial Function withGiven Zeros In Exercises 59–64, find apolynomial function with real coefficientsthat has the given zeros. (There are manycorrect answers.)59. 1, 5i60. 4, −3i61. 2, 2, 1 + i62. −1, 5, 3 − 2i63. 23, −1, 3 + √2i64. −52, −5, 1 + √3i
Let a, be the leading coefficient
(a) Find the complete factored form of a polynomial with real coefficients f(x) that satisfies the conditions.
(b) Express f(x) in expanded form.
degree 2; a, = 1, zeros 2i and - 21
(a) f(x) =
(Simplify your answer. Type your answer in factored form. Express complex numbers in terms of i.)
(b) f(x) =
(Simplify your answer.)
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