Question

Which of the following statements is true

Answer 1

Answer:

  c. This quadratic equation has two complex solutions.

Step-by-step explanation:

Of the choices ...

  a. This quadratic equation has exactly one real solution.

  b. This quadratic equation has two real solutions.

  c. This quadratic equation has two complex solutions.

  d. This quadratic equation has no solutions.

The one that is true is c: two complex solutions.

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The discriminant of quadratic ax^2 +bx +c = 0 is ...

  d = b^2 -4ac

For this quadratic, the value is 6^2 -4·5·2 = -4.

When the discriminant is positive, there are two distinct real solutions.

When the discriminant is zero, there is one real solution.

When the discriminant is negative, there are two complex solutions. The discriminant of this quadratic is negative, so there are two complex solutions.