Question

Find all values of n for which the equation has two complex (non-real solutions)

6r² = 8r+ (n + 4)

Answer 1

• 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:

• D = b² - 4ac

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