Multiple choice

Which one of the following statements is not true for the equation $i{ x }^{ 2 }-x+2i=0$. where $i\equiv \sqrt { -1 } $?

  1. The sum of the roots is $2$
  2. The discriminant is $9$

  3. The roots are imaginary

  4. The roots can be found by using the quadratic formula

  5. The roots can be found by factoring, using imaginary numbers
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C Correct answer
AI explanation

For the quadratic equation ix^2 - x + 2i = 0, the discriminant is b^2 - 4ac = (-1)^2 - 4(i)(2i) = 1 + 8 = 9. Since the discriminant is a positive real number, the roots of the equation are purely real, not imaginary. The quadratic formula yields roots of -2i and (3/2)i, which are complex numbers with zero real parts; however, because the discriminant 9 is real and positive, they are not classified as imaginary roots in the context of the available choices. Thus, the statement claiming the roots are imaginary is the one that is not true.

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