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Leya [2.2K]
3 years ago
8

Can someone please help me with this problem ASAP thank you

Mathematics
1 answer:
Step2247 [10]3 years ago
6 0

3-degree polynomial is f(x )= [x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]

Step-by-step explanation:

Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x= \frac{9}{7} and x= -3i

In order to find the equation of a 3-degree polynomial, we need 3 roots.

Here, One of Root is real number x=\frac{9}{7} and another root is an imaginary number x=(-3i)

It is necessary to note that imaginary roots always come in pair of conjugates

Therefore, Comjugate0 of x =(-3i) is 3rd root

Conjugate of (-3i) is 3i

Evaluting equation of polynomial,

=[x-3i][x+3i][x-\frac{9}{7} ]

=[x^{2}-(3i)^{2}][x-\frac{9}{7} ]

=[x^{2}-(9)(i)^{2}][x-\frac{9}{7} ]

=[x^{2}+9][x-\frac{9}{7} ]

f(x )= [x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ]

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The graphs shown below confirm these results.

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