Question

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.

Answer 1

Given equation:

`(3x-4i)(7x-8)(3x+4i)=0`

i.e.,
`3x-4i=0` and
`7x-8=0` and
`3x+4i=0`

i.e.,
`3x=4i` and
`7x=8` and
`3x=-4i`

i.e.,
`x=(4i)/(3)` and
`x=(8)/(7)` and
`x=-(4i)/(3)`

Therefore, the given equation has a real root i.e.,
`x=(8)/(7)`

and two complex conjugate roots i.e.,
`x=(4i)/(3)` and
`x=-(4i)/(3)`

Hence, option C is correct.