Math Problem Statement
Find a degree 3 polynomial with a leading coefficient of 1, and zeros -1,
−
3
i
, and
3
i
. Simplify your answer so that it has only real numbers as coefficients. Be sure to write the full equation, including
P
(
x
)
.
Solution
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Math Problem Analysis
Mathematical Concepts
Algebra
Polynomials
Complex Numbers
Real Coefficients
Formulas
P(x) = (x + 1)(x + 3i)(x - 3i)
(x + 3i)(x - 3i) = x^2 + 9
P(x) = (x + 1)(x^2 + 9) = x^3 + x^2 + 9x + 9
Theorems
Difference of squares: (a + b)(a - b) = a^2 - b^2
Complex conjugate root theorem
Suitable Grade Level
Grades 10-12
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