Find a polynomial function with real coefficients that has the given zeros. 2,4 + 3i A)x³ - 10x² + 41x + 50 B)x³ + 10x² + 41x + 50 C)x³ - 10x² + 41x - 50 D)x³ - 10x² - 41x - 50 E)x³ + 10x² + 41x - 50

Question

Quizplus · Accepted Answer

The given zeros are 2, 4+3i, and 4-3i (since complex zeros always come in conjugate pairs). Therefore, the polynomial function can be expressed as: 
(x-2)(x-(4+3i))(x-(4-3i)) 
Simplifying this expression: 
(x-2)[x-4-3i][x-4+3i] 
(x-2)[(x-4) - 3i][(x-4) + 3i] 
(x-2)(x-4)^2 - (3i)^2 
(x-2)(x-4)^2 + 9 
Expanding this out further: 
(x^3 - 10x^2 + 41x - 50) 
Therefore, the correct choice is C, x^3 - 10x^2 + 41x - 50.

Find a Polynomial Function with Real Coefficients That Has the Given