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Princess Poly claims that the equation (3x−4i)(7x−8)(3x+4i)=0 has three roots, a real root and a complex root with a multiplicity of 2.

Which statement regarding her claim is true?


A) Princess Poly is correct. The equation has exactly three roots, one real root, x=87, and one complex root with a multiplicity of 2, x=43i.

B) Princess Poly is not correct. The equation has exactly three roots, one real root, x=−87, and two complex roots, x=43i and x=−43i.

C) Princess Poly is not correct. The equation has exactly three roots, one real root, x=87, and two complex roots, x=43i and x=−43i.

D) Princess Poly is correct. The equation has exactly three roots, one real root, x=87, and one complex root with a multiplicity of 2, x=−43i.

Respuesta :

Given equation:

[tex](3x-4i)(7x-8)(3x+4i)=0[/tex]

i.e., [tex]3x-4i=0[/tex]       and       [tex]7x-8=0[/tex]       and       [tex]3x+4i=0[/tex]

i.e., [tex]3x=4i[/tex]       and       [tex]7x=8[/tex]       and       [tex]3x=-4i[/tex]

i.e., [tex]x=\frac{4i}{3}[/tex]       and       [tex]x=\frac{8}{7}[/tex]       and       [tex]x=-\frac{4i}{3}[/tex]

Therefore, the given equation has a real root i.e., [tex]x=\frac{8}{7}[/tex]

and two complex conjugate roots i.e., [tex]x=\frac{4i}{3}[/tex] and [tex]x=-\frac{4i}{3}[/tex]

Hence, option C is correct.

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