Answer:
- When n < - 6 2/3 the given equation has two complex solutions
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Given is a quadratic equation:
- 6r² = 8r+ (n + 4) ⇒ 6r² - 8r - (n + 4) = 0
A quadratic equation has no real solutions if its discriminant is negative.
The discriminant of ax² + bx + c is:
Apply to given equation:
- D = (-8)² - 4*6*( - (n + 4)) = 64 + 24(n + 4) = 64 + 24n + 96 = 24n + 160
Find the value of n when D < 0:
- 24n + 160 < 0
- 24n < - 160
- n < - 160/24
- n < - 20/3
- n < - 6 2/3
