129k views
4 votes
I really need help please!

I really need help please!-example-1
User Depquid
by
6.9k points

1 Answer

4 votes

Answer:

n < -15/4

Explanation:

You want to use the discriminant to find the values of n for which the quadratic 3z² -9z = (n -3) has only complex solutions.

Discriminant

The discriminant of quadratic equation ax²+bx+c = 0 is ...

d = b² -4ac

The given quadratic can be put in this form by subtracting (n-3):

3z² -9z -(n -3) = 0

This gives us ...

  • a = 3
  • b = -9
  • c = -(n -3)

and the discriminant is ...

d = (-9)² -4(3)(-(n-3)) = 81 +12(n -3)

d = 12n +45

Complex solutions

The equation will have only complex solutions when the discriminant is negative:

d < 0

12n +45 < 0 . . . . . use the value of the discriminant

n +45/12 < 0 . . . . . divide by 12

n < -15/4 . . . . . . . subtract 15/4

There will be two complex solutions when n < -15/4.

User David Oganov
by
7.7k points