Can someone please help me with this problem ASAP thank you
Question
Answer:
3-degree polynomial is f(x )= [tex][x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ][/tex]Step-by-step explanation:Given that polynomial f(x) is 3-degree polynomial and Zeros/Roots at x= [tex]\frac{9}{7}[/tex] and x= -3iIn order to find the equation of a 3-degree polynomial, we need 3 roots.Here, One of Root is real number x=[tex]\frac{9}{7}[/tex] and another root is an imaginary number x=(-3i)It is necessary to note that imaginary roots always come in pair of conjugatesTherefore, Comjugate0 of x =(-3i) is 3rd root Conjugate of (-3i) is 3iEvaluting equation of polynomial,=[tex][x-3i][x+3i][x-\frac{9}{7} ][/tex]=[tex][x^{2}-(3i)^{2}][x-\frac{9}{7} ][/tex]=[tex][x^{2}-(9)(i)^{2}][x-\frac{9}{7} ][/tex]=[tex][x^{2}+9][x-\frac{9}{7} ][/tex]f(x )= [tex][x^{3 }-\frac{9}{7} x^{2}+9x-\frac{81}{7} ][/tex]
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10 months ago
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