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If the equation a x 2 + 2 b x - 3 c = 0 has no real roots and 3 c 4 < a + b , then

Options

Ac < 0
Bc > 0
Cc = 0
Da + 2 b - 3 c < 0

Correct answer

A. c < 0

Step-by-step solution

a x 2 + 2 b x - 3 c = 0 has no real roots f 2 = 4 a + 4 b - 3 c = 4 a + b - 3 c 4 > 0 (given) So, f x > 0   ∀ x ⇒ f 0 > 0 ⇒ - 3 c > 0 ⇒ c < 0

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